// Numbas version: exam_results_page_options {"name": "End of Year IB1 Exam SL", "metadata": {"description": "Exam paper at end of year for IB1 SL students.", "licence": "All rights reserved"}, "duration": 5700, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Demo Question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "Question to start exam paper to allow everyone to practice with software.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

This is just a demonstration question to ensure everyone is using the software correctly.

This is just a demonstration question, none of your answers count towards your final grade but you may like to compare your predicted percentage with the percentage you achieved on this test.

", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1 .. 10#1)", "description": "

", "templateType": "randrange"}, "pie": {"name": "pie", "group": "Ungrouped variables", "definition": "pi", "description": "

pi

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Most questions will require you to answer with a number. Enter a number between 1 and 10 below and press Submit part.

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If you get the correct answer you will get a mark. Enter the number 1 below and press Submit part.

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Some questions will require an equation. Enter x = 3 below and press Submit part.

", "answer": "x[]*=[]*3", "displayAnswer": "x[]*=[]*3", "matchMode": "regex"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

In other questions, you will be penalised for not rounding correctly. For example, write the number $3.142$ in the space below and press Submit part

\n

$\\pi =$ [[0]]

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\n
• \n
"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

In the rest of the questions, you will not be told if your answer is right or wrong until completing the exam.

\n

Write your prediction for the percentage you will score on this test below and press Submit. Note that you are not informed if this is correct or not.

\n

I think I will score [[0]] $\\%$

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\n
• You can also submit all answers to a question at the bottom of each page. Press Submit all parts now and you will be taken to the next question. No answers on this page will count towards your final grade.
• \n
"}]}, {"name": "Arithmetic Sequences - Common Difference and Term", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "Based on first and second term of an arithmetic sequence find common difference and eighth term.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

In an arithmetic sequence the first term is {a} and the second term is {b}.

The common difference is the difference between any two consecutive terms. In this case the first and second term.

\n

\n

common difference = $\\var{b} - \\var{a} = \\var{d}$

\n

\n

To find any term in a sequence use the formula $u_n = u_1 + (n-1)d$

\n

In this case $u_8 = \\var{a} + 7 \\times \\var{d} = \\var{a + 7d}$

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first term

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common difference (restricted to small integers)

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second term based on common difference.

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Find the common difference.

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Find the eighth term.

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In an arithmetic sequence the {term_a} term is {u_a} and the {term_b} is {u_b}.

In part (a) you should divide the difference between the {term_b} term and the {term_a} term by {n}

\n

({u_b}-{u_a})/{n} = {d}

\n

In part (b) use the formula

\n

$u_n = u_1 + (n-1)d$

\n

and rearrange to find $u_1$ either using the {term_a} or {term_b} term and calculated value of $d$

\n

$u_1 =$ {u_1}

\n

In part c use the formula for the sum of n terms of an arithmetic sequence

\n

$S_n = \\frac{n}{2}(2u_1+(n-1)d)$

\n

In this case the sum of the first {number_sum} terms is

\n

= ({terms_to_sum}/2) x (2 x {u_1} + ({terms_to_sum} - 1) x {d}))

\n

= {sum_val}

\n

", "rulesets": {}, "variables": {"term_a": {"name": "term_a", "group": "Ungrouped variables", "definition": "\"{terms_eng[{a}-1]}\"", "description": "

english word for the term number given first in problem.

", "templateType": "string"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3 .. 7#1)", "description": "

number of smaller term given in problem.

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list to convert numbers to word for term

", "templateType": "list of strings"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "

Common difference in this sequence.

", "templateType": "randrange"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "

difference in terms of number of terms

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value of ath term

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First term in this sequence

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term number of larger term in sequence

", "templateType": "anything"}, "u_b": {"name": "u_b", "group": "Ungrouped variables", "definition": "{u_1}+({b}-1)*{d}", "description": "

value of bth term

", "templateType": "anything"}, "term_b": {"name": "term_b", "group": "Ungrouped variables", "definition": "\"{terms_eng[{b}-1]}\"", "description": "

term number in words

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table to convert numbers to words

", "templateType": "list of strings"}, "terms_to_sum": {"name": "terms_to_sum", "group": "Ungrouped variables", "definition": "random(15 .. 25#5)", "description": "

variable denoting how many terms should be summed (always a multiple of 5)

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terms_to_sum converted to words

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evaluation of sum of appropriate number of terms

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Find the common difference.

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Find the first term.

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Find the sum of the first {number_sum} terms.

", "minValue": "{sum_val}", "maxValue": "{sum_val}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Evaluating a function 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "Substituting a (negative) value into a function involving a quqdratic and 1/x", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Consider the function $f(x) =${a}$x^2 - \\frac{8}{x}, x \\ne 0$

This question is testing that you can substitute the value given into the function. If your result does not match the answer given, {f_eval}, then check the following

\n
\n
• When squaring a negative number the result is positive
• \n
• It is important to perform operations in the correct order, multiplying by {eval} by {a} and then squaring the result is not the same as squaring {eval} and then multiplying by {a}
• \n
\n

", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(0.5 .. 2.5#0.5)", "description": "

coefficient of x^2 in function

", "templateType": "randrange"}, "eval": {"name": "eval", "group": "Ungrouped variables", "definition": "random(-4 .. -2#2)", "description": "

point at which function should be evaluated

", "templateType": "randrange"}, "f_eval": {"name": "f_eval", "group": "Ungrouped variables", "definition": "{a}*eval^2 - 8/eval", "description": "

result of evaluating function at given point

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "eval", "f_eval"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Evaluate $f(${eval}$)$

", "minValue": "{f_eval}", "maxValue": "{f_eval}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Functions - Intersections", "extensions": [], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "

The answer is a comma-separated list of numbers.

\n

The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.

", "name": "bits", "definition": "filter(x<>\"\",x,split(studentAnswer,\",\"))"}, {"description": "", "name": "expected_numbers", "definition": "settings[\"correctAnswer\"]"}, {"description": "

Is every number in the student's list valid?

", "name": "valid_numbers", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n true,\n let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n warn(wrong+\" is not a valid number\");\n fail(wrong+\" is not a valid number.\")\n )\n )"}, {"description": "

Are the student's answers in ascending order?

Is each number in the expected answer present in the student's list the correct number of times?

", "name": "included", "definition": "map(\n let(\n num_student,len(filter(x=y,y,interpreted_answer)),\n num_expected,len(filter(x=y,y,expected_numbers)),\n switch(\n num_student=num_expected,\n true,\n num_studentHas every number been included the right number of times?

", "name": "all_included", "definition": "all(included)"}, {"description": "

True if the student's list doesn't contain any numbers that aren't in the expected answer.

Consider the function $f(x) = x +$ {a}, and $g(x) =$ {b}$^x - 2$.

In part (a) the x-intercept is when y is zero

\n

Solve $0 = x +$ {a}

\n

$x =$ {neg_a}

\n

must be given as a coordinate ({neg_a},0)

\n

In part (b) the y-intercept is when x is zero. and remember any number to the power zero is one,   $a^0 = 1$

\n

$y = 1 - 2 = -1$

\n

must be given as a coordinate (0,-1)

\n

In part (c) you should sketch the graph on your GDC and find the intersections of the two graphs. These should be at {sol_1} and {sol_2}.

", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1 .. 5#1)", "description": "

constant term in linear function f(x)

", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "3", "description": "

Base in exponential function g(x)

", "templateType": "number"}, "poss_sol_1": {"name": "poss_sol_1", "group": "Ungrouped variables", "definition": "[ -2.96, -3.99, -5, -6, -7 ]", "description": "

possible solutions based on a

", "templateType": "list of numbers"}, "sol_1": {"name": "sol_1", "group": "Ungrouped variables", "definition": "poss_sol_1[a-1]", "description": "

solution 1

", "templateType": "anything"}, "poss_sol_2": {"name": "poss_sol_2", "group": "Ungrouped variables", "definition": "[ 1.34, 1.56, 1.74, 1.88, 2 ]", "description": "", "templateType": "list of numbers"}, "sol_2": {"name": "sol_2", "group": "Ungrouped variables", "definition": "poss_sol_2[a-1\n]", "description": "", "templateType": "anything"}, "neg_a": {"name": "neg_a", "group": "Ungrouped variables", "definition": "-a", "description": "

negative of a

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "poss_sol_1", "sol_1", "poss_sol_2", "sol_2", "neg_a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the x-intercept of $f(x)$.

\n

([[0]],[[1]])

Find the y-intercept of $g(x)$.

\n

\n

([[0]],[[1]])

The equation $f(x) = g(x)$ has two solutions. Write them both below

", "settings": {"correctAnswer": "[sol_1,sol_2]", "allowFractions": false, "correctAnswerFractions": false}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Geometric Sequences - First three terms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "From first three terms find common ratio, n for specified u_n  and sum terms.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

The first three terms of a geometric sequence are $u_1 =$ {u_1},  $u_2 =$ {u_2} and $u_3 =$ {u_3}.

In part (a) the common ration can be found by dividing a term by the preceding term. Either $\\frac{u_3}{u_2}$ or $\\frac{u_2}{u_1}$

\n

$r = 1 \\div$ {reciprocal_r}

\n

In part (b) use the formula $u_n = u_1r^{n-1}$ and substitute value for $r$ and $u_1$ and set $u_n = 2$

\n

2 = {u_1}/{reciprocal_r}$^{n-1}$

\n

{reciprocal_r}$^{n-1} =$ {u_1} $\\div 2 =$ {half_u_1}

\n

This is a 'nice' power of {reciprocal_r}

\n

$n - 1 = 5$

\n

$n = 6$

\n

In part (c) use the formula $S_n = \\frac{u_1(1-r^n)}{1-r}$ it is preferable in this case since $|r|<1$

\n

substituting values that you know gives sum of first {how_many} terms to be {sum_c}

\n

", "rulesets": {}, "variables": {"u_3": {"name": "u_3", "group": "Ungrouped variables", "definition": "u_6*{reciprocal_r}^3", "description": "

Third term of the geometric sequence

", "templateType": "anything"}, "reciprocal_r": {"name": "reciprocal_r", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "

reciprocal of the common ratio.

", "templateType": "randrange"}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "1/{reciprocal_r}", "description": "

common ratio, set to be a fraction either $\\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}, \\frac{1}{5}$ or $\\frac{1}{6}$

", "templateType": "anything"}, "u_2": {"name": "u_2", "group": "Ungrouped variables", "definition": "{u_3}*{reciprocal_r}", "description": "

Second term of the geometric sequence

", "templateType": "anything"}, "u_1": {"name": "u_1", "group": "Ungrouped variables", "definition": "{u_2}*{reciprocal_r}", "description": "

First term of the geometric sequence

", "templateType": "anything"}, "u_6": {"name": "u_6", "group": "Ungrouped variables", "definition": "2", "description": "

Sixth term of geometric sequence

", "templateType": "number"}, "how_many": {"name": "how_many", "group": "Ungrouped variables", "definition": "random(20 .. 30#5)", "description": "

Variable to determine how many terms should be summed in part (c)

", "templateType": "randrange"}, "sum_c": {"name": "sum_c", "group": "Ungrouped variables", "definition": "u_1*(1- r^how_many)/(1-r)", "description": "

Answer to part (c), summing appropriate number of terms

", "templateType": "anything"}, "half_u_1": {"name": "half_u_1", "group": "Ungrouped variables", "definition": "u_1/2", "description": "

u_1 divided by u_6 required in advice.

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["u_3", "reciprocal_r", "r", "u_2", "u_1", "u_6", "how_many", "sum_c", "half_u_1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $r$ the common ratio.

", "minValue": "{r}", "maxValue": "{r}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $n$ for which $u_n =$ {u_6}.

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Find the sum of the first {how_many} terms of the sequence.

", "minValue": "{sum_c}", "maxValue": "{sum_c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Interpreting quadratic - with graph", "extensions": [], "custom_part_types": [], "resources": [["question-resources/parabola1.png", "/srv/numbas/media/question-resources/parabola1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "A graph is given with one intercept (negative) and a vertex (positive x and y) and from this students should be able to ascertain the axis of symmetry and equation (given that the leading coefficent of x is -1)", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

The graph of the quadratic function $f(x) = c + bx - x^2$ intersects the $x$-axis at the point A = ({x_int1},0) and has it's vertex at point B = ({x_vert},{y_vert})

\n

In part (a) you can calculate the axis of symmetry from the x-coordinate of the vertex {x_vert}. Don't forget to put in the form of an equation for a vertical line.

\n

$x =$ {x_vert}

\n

In part (b) use the formula that the axis of symmetry has equation $x = \\frac {-b}{2a}$. Rearranging and substituting a with -1.

\n

$b = 2 \\times${x_vert}

\n

$b =$ {b}

\n

In part (c) you now know the value of $b$ and have two coordinates to work with, so you can find $c$ by substitution.

\n

EITHER

\n

$0 = c +$ {b} $\\times${x_int1} $-(${x_int1}$)^2$

\n

$c = ($ {x_int1}$)^2$ $-${b}$\\times${x_int1}

\n

$c =$ {c}

\n

OR

\n

{y_vert} $= c +$ {b} $\\times${x_vert} $-${x_vert}$^2$

\n

$c =$ {x_vert}$^2$ $-${b}$\\times${x_vert} $+$ {y_vert}

\n

$c =$ {c}

", "rulesets": {}, "variables": {"x_int1": {"name": "x_int1", "group": "Ungrouped variables", "definition": "random(-6 .. -1#1)", "description": "

left intercept with the x-axis, must be negative to agree with diagram.

", "templateType": "randrange"}, "x_vert": {"name": "x_vert", "group": "Ungrouped variables", "definition": "random(2 .. 4#1)", "description": "

x-coordinate of vertex, must be positive to agree with diagram.

", "templateType": "randrange"}, "x_int2": {"name": "x_int2", "group": "Ungrouped variables", "definition": "2*x_vert - x_int1", "description": "

right intercept with the x-axis, calculated based on vertex

", "templateType": "anything"}, "y_vert": {"name": "y_vert", "group": "Ungrouped variables", "definition": "-(x_vert - x_int1)*(x_vert - x_int2)", "description": "

y - coordinate of vertex, calculated from intercepts and leading coefficient of $x^2$ being -1

", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "2*x_vert", "description": "

coefficient of x

", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "-x_int1*x_int2", "description": "

constant term

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x_int1", "x_vert", "x_int2", "y_vert", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the equation of the axis of symmetry of $f$

", "answer": "x[ ]*=[ ]*{x_vert}", "displayAnswer": "x = {x_vert}", "matchMode": "regex"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $b$.

", "minValue": "{b}", "maxValue": "{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $c$.

", "minValue": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Intersection of graphs - graphically", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "Find intersection of two graphs using GDC.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Let $f(x) = xe^{-x}$ and $g(x) = -3f(x) +1$.

\n

The graphs of $f$ and $g$ intersect at $x=p$ and $x=q$ where $p<q$.

\n

This problem should be solved by sketching the graphs on your graphics calculator and using the intersect option to find where they cross.

\n

The two values are

\n

$p =$ {p} and

\n

$q =$ {q}

\n

but note that answers should be given o 3 significant figures

\n

$p = 0.357$ and

\n

$q = 2.15$

\n

you may have been penalised if you rounded incorrectly.

", "rulesets": {}, "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "0.357403", "description": "

Intersection 1.

", "templateType": "number"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "2.1532924", "description": "

Intersection 2

", "templateType": "number"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["p", "q"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Write down the value of $p$.

", "minValue": "p", "maxValue": "p", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Write down the value of $q$.

", "minValue": "q", "maxValue": "q", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Linear Functions 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "Rearrange to give for y = mx + c, find gradient and realise that a parallel line has the same gradient (find x_intercept)", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

The equation of a line $L$ is {a}$x + y =${y_int}

In part (a) rearrange the equation in the form $y = mx + c$

\n

$y = -${a}$x +$ {y_int}

\n

\n

In part (b) the y intercept is at (0,{y_int})

\n

In part (c) the equation of the new line is $y =$ {grad}$x +$ {y_int2}, substituting y to be zero will give the x-intercept at ({M_x},{M_y})

", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "

a in equation ax + y = c

", "templateType": "randrange"}, "y_int": {"name": "y_int", "group": "Ungrouped variables", "definition": "random(-3 .. 4#1)", "description": "

y intercept of straight line

", "templateType": "randrange"}, "grad": {"name": "grad", "group": "Ungrouped variables", "definition": "-{a}", "description": "

", "templateType": "anything"}, "y_int2": {"name": "y_int2", "group": "Ungrouped variables", "definition": "random(2 .. 9#1)", "description": "

y intercept of second parallel line

", "templateType": "randrange"}, "M_x": {"name": "M_x", "group": "Ungrouped variables", "definition": "{y_int2}/(-{grad})", "description": "

x-intercept of second parallel line

", "templateType": "anything"}, "M_y": {"name": "M_y", "group": "Ungrouped variables", "definition": "0", "description": "

y coordinate at x-intercept of second line

", "templateType": "number"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "y_int", "grad", "y_int2", "M_x", "M_y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Write down the gradient of line $L$.

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Complete below to give the y-intercept of line $L$

\n

(0,[[0]])

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{y_int}", "maxValue": "{y_int}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

A second line M is parallel to L and passes through point P(0,{y_int2})

\n

\n

The line M intercepts the x-axis at ([[0]],[[1]])

The number of apartments in a housing development has been increasing by a constant amount every year. At the end of the first year, the number of apartments was {u_1}, and at the end of the {years} year, the number of apartments was {u_years}. The number of apartments, $y$, can be determined by the equation $y = mt + n$,  where $t$ is the time, in years.

$m$ is the gradient of the line, it is also the common difference in the arithmetic sequence so you can use the formula $u_n = u_1 + (n-1)d$

\n

In this case $n =$  {n} so {u_years} = {u_1} + ({n}-1) $\\times d$

\n

m = {u_years - u_1} $\\div$ {n-1}

\n

m = {d}

\n

$n$ represents the situation at the beginning of year 1, so is $u_1 - d$

\n

$n =$ {u_1} - {d}

\n

$n =$ {u_0}

\n

", "rulesets": {}, "variables": {"u_1": {"name": "u_1", "group": "Ungrouped variables", "definition": "{u_0}+d", "description": "

first term (houses at end of first year)

", "templateType": "anything"}, "years_eng": {"name": "years_eng", "group": "Ungrouped variables", "definition": "[ \"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\", \"tenth\" ]", "description": "

conversion list for number of years to english

", "templateType": "list of strings"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(5 .. 8#1)", "description": "

number of years at which second number of houses is given

", "templateType": "randrange"}, "years": {"name": "years", "group": "Ungrouped variables", "definition": "\"{years_eng[{n}-1]}\"", "description": "

n converted to word

", "templateType": "string"}, "u_years": {"name": "u_years", "group": "Ungrouped variables", "definition": "{u_1}+({n}-1)*{d}", "description": "

u_n number of houses after n years

", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(60 .. 110#10)", "description": "

common difference to apply

", "templateType": "randrange"}, "u_0": {"name": "u_0", "group": "Ungrouped variables", "definition": "random(40 .. 120#10)", "description": "

first term of sequence (houses at start of first year)

", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["u_1", "years_eng", "n", "years", "u_years", "d", "u_0"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $m$.

", "minValue": "{d}", "maxValue": "{d}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $n$.

", "minValue": "{u_0}", "maxValue": "{u_0}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Quadratic Functions 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "tags": [], "metadata": {"description": "Finding parameters of a factorised quadratic based on x-intercepts at vertex. Function has one intercept at origin and one at a positive integer value. Constant multiplier is randomised and requires vertex in order to calculate.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Consider the quadratic function, $f(x) = px (q−x)$, where $p$ and $q$ are positive integers. The graph of $y = f(x)$ passes through the point ({q}, 0).

In part (a) note that the factorised form of the equation gives the two vertices. Evaluate when the function is zero.

\n

This occurs at the origin and when $x = q$. Therefore $q =$ {q}

\n

In part (b) $p$ can be evaluated by substituting the values of $x$ and $y$ at the vertex into the equation.

\n

{ver_y} $= p \\times${ver_x}$(${q} $-$ {ver_x}$)$

\n

$p =$ {ver_y} $\\div [${ver_x}$\\times(${q} $-$ {ver_x}$)]$

\n

$p =$ {p}

\n

In part (c) note that the coefficient of $x^2$ is negative and therefore the parabola is concave down.

\n

The range can be calculated from the y-coordinate of the vertex since this is a maximum point.

\n

$y \\leq$ {ver_y}

", "rulesets": {}, "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(1 .. 6#1)", "description": "

p in equation px(q-x)

", "templateType": "randrange"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(1 .. 6#1)", "description": "

q in equation px(q-x)

", "templateType": "randrange"}, "ver_x": {"name": "ver_x", "group": "Ungrouped variables", "definition": "{q}/2", "description": "

x-coordinate of vertex, based on q

", "templateType": "anything"}, "ver_y": {"name": "ver_y", "group": "Ungrouped variables", "definition": "{p}*{ver_x}*({q}-{ver_x})", "description": "

y coordinate of vertex, based on substitution into the formula.

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["p", "q", "ver_x", "ver_y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $q$.

", "minValue": "{q}", "maxValue": "{q}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The vertex of the function is at ({ver_x},{ver_y}).

"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the value of $p$.

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Which of the following is the range of $f(x)$

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Let $f(x) = x^2 -${b}$x +${c}

When completing the square the value of $h$ can be found by dividing {b} by 2.

\n

$h =$ {h}

\n

To find $k$, try expanding the bracket and notice what is required to correct the constant term.

\n

$(x-${h}$)^2 = x^2 - 2\\times${h}$x +${h}$^2$

\n

Therefore $k =$ {c} $-${h}$^2$

\n

$k =$ {k}

", "rulesets": {}, "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "2*h", "description": "

coefficient of x is negative this value.

", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "h^2+k", "description": "

", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(1 .. 5#1)", "description": "

h when completing the square and giving function in form (x-h)^2 + k

", "templateType": "randrange"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(2 .. 8#1)", "description": "

k when completing the square and giving function in form (x-h)^2 + k

", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b", "c", "h", "k"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Write the function in the form $f(x) = (x-h)^2 + k$      $h,k \\in$$Z^+$

\n

\n

$f(x) = (x-$[[0]]$)^2 +$ [[1]]

The following diagram shows the graph of a function $f$, with domain $-2 \\leq x \\leq 4$

\n

\n

The points $(-2,0)$ and $(4,7)$ lie on the graph of $f$.

In part (a) remember that the range refers to the possible y values and so the correct answer is $0 \\leq y \\leq 7$ don't forget to use less than or equal to signs.

\n

In part (b) you should find the y-coordinate on the graph corresponding to the x-coordinate {a}. In this case {f_a}

\n

In part (c) you are dealing with the inverse function and so should do the reverse. Given y-coordinate {b} find the corresponding x-coordinate {finvb}.

", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "x_coord[randomiser_1]", "description": "", "templateType": "anything"}, "randomiser_1": {"name": "randomiser_1", "group": "Ungrouped variables", "definition": "random(0 .. 4#1)", "description": "

number to randomise question b

", "templateType": "randrange"}, "f_a": {"name": "f_a", "group": "Ungrouped variables", "definition": "y_coord[randomiser_1]", "description": "", "templateType": "anything"}, "y_coord": {"name": "y_coord", "group": "Ungrouped variables", "definition": "[ 0, 2, 3, 4, 7 ]", "description": "", "templateType": "list of numbers"}, "randomiser_2": {"name": "randomiser_2", "group": "Ungrouped variables", "definition": "random(0 .. 4#1)", "description": "

number to randomise question c

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Which of the following is the correct expression for the domain of $f$?

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Write down $f( \\var{a} )$.

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Write down $f^{-1}( \\var{b} )$.

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Let $f(x) = p + \\frac{3}{x-q}, x \\ne$ {q}.

Parts (a) and (b) both relate to the vertical asymptote. This occurs when the denominator in the fraction $x -${q} = 0

\n

Therefore q = {q} and the vertical asymptote is at $x =$ {q}

\n

Part (c) is about the y-intercept. This is when $x = 0$

\n

$f(0) = p + \\frac{3}{-3}$

\n

$f(0) = p - 1$

\n

$p - 1=$ {p-1}

\n

$p=$ {p}

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q in function, determines vertical asymptote.

", "templateType": "number"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2 .. 7#1)", "description": "

p in function, determines y-intercept

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Write down the value of $q$

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Write down the value of the vertical asymptote.

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The graph intercepts the y-axis at the point (0,{p-1})

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Write down the value of $p$

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Assume that the Earth is a sphere with a radius, $r$ , of $6.38 \\times10^3 km$.

\n

In this question use the formula for the surface area of a sphere.

\n

$A = 4\\pi r^2 \n This should return a value of {s_area_act} on your calculator \n rounded to three significant figures this is {s_area} \n In standard form this is$5.12 \\times 10^8$\n You may have received credit for writing your (a) in standard form correctly. 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She is visiting the Grand Canyon. When she reaches the top, she drops a coin down a cliff. The coin falls down a distance of {u_1} metres during the first second, {u_2} metres during the next second, {u_3} metres during the third second and continues in this way. The distances that the coin falls during each second forms an arithmetic sequence. ", "advice": " Parts (a) - (d) involve an arithmetic sequence. \n In part (a) the common difference is the difference between any two consecutive terms. Either$u_2 - u_1$or$u_3 - u_2$. These both evaluate to give$d = 10 $metres. \n In part (b) you can find the fourth term by adding d to the thrìird term$u_4 = u_3 + d = \\var{u_3} + 10 = \\var{u_4}$. \n In part (c) you should apply the formula$u_n = u_1 + (n-1)d$. \n In this case you are finding the {nth} term so$u_\\var{n} = u_1 + (\\var{n}-1)d$\n$u_\\var{n} = \\var{u_1} + (\\var{n}-1) \\times \\var{d} = \\var{u_n}$\n In part (d) you are now summing terms so should use the formula for an arithmetic sequence$S_n = \\frac{n}{2}(2u_1 + (n-1)d)$or alternatively since you have just found$u_\\var{n}$you could use$S_n = \\frac{n}{2}(u_1 + u_n)$\n In this case$S_\\var{n} = \\frac{\\var{n}}{2}( \\var{u_1} + \\var{u_n}) = \\var{1000*S_n}$metres which corresponds to$\\var{S_n}$kilometres. \n In parts (e) and (f) you are given information about a geometric sequence with first term$\\var{visitors}$and common ratio given by$1 + \\frac{\\var{p}}{100} = \\var{1 + p/100}$. \n In (e) the number of visitors in 2016 is$\\var{visitors} \\times \\var{1 + p/100} = \\var{visits_2016} $. You may have rounded this answer to 3 significant figures. \n In (f) you are now summing the first ten terms and should use the formula$S_n = \\frac  {u_1(r^n -1 )}{r-1}$\n$S_{10} = \\frac{\\var{visitors} \\times (\\var{1 + p/100}^{10}-1)}{\\var{1 + p/100}-1}$\n This value should be rounded to 3 significant figures giving$S_{10}=\\var{visits_10y_rounded}\$.

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first term

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common difference

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second term

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third term

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fourth term

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number of terms to sum

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nth term

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sum of n terms

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Number of visitors in 2015

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p% increase in visitors expected.

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visitors in 2016

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visitors in first ten years.

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minimum accepted answer to part (e) since result may be rounded or given exactly.

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maximum accepted answer to part (e) since result may be rounded or given exactly.

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10 year visits rounded to 3 significant figures.

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["u_1", "d", "u_2", "u_3", "u_4", "n", "u_n", "S_n", "number_eng", "nth", "visitors", "p", "visits_2016", "visits_10y", "min_visits_2016", "max_visits_2016", "visits_10y_rounded"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the common difference (in metres) of this arithmetic sequence.

", "minValue": "d", "maxValue": "d", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What distance (In metres) does the coin fall in the fourth second.

", "minValue": "u_4", "maxValue": "u_4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What distance (in metres) does the coin fall in the {nth} second.

", "minValue": "u_n", "maxValue": "u_n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the distance in kilometres that the coin falls in the first {n} seconds.

", "minValue": "S_n", "maxValue": "S_n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Prachi visits a tourist centre nearby. It opened at the start of 2015 and in the first year there were {visitors} visitors. The number of people who visit the tourist centre is expected to increase by {p}% each year.

"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the number of visitors expected to visit the tourist centre in 2016.

", "minValue": "min_visits_2016", "maxValue": "max_visits_2016", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the number of people expected to visit the tourist centre in the first ten years since it opened.

", "minValue": "visits_10y", "maxValue": "visits_10y", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "onleave": {"action": "none", "message": "

If you have answers for this question do not forget to press Submit so that values will be recorded.

"}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "warn", "message": "

The exam has now finished.

"}, "timedwarning": {"action": "warn", "message": "

There are five minutes remaining

You have five minutes to read through questions.

\n

You will then have 90 minutes to complete this exam.

\n

After answering a question (or part of the question) you must press submit for your answer to be saved. Be careful, if you do not press submit on each question you will score zero. Before exiting the exam you should check you have submitted all answers.

\n

You may use a calculator throughout this examination.

\n

After finishing the exam you will be provided with immediate feedback. You should download this document and submit to the task on ManageBac so your teacher can review your paper.

\n

Unless stated otherwise answers should be given exactly or to 3 significant figures where appropriate.

", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [{"message": "

", "threshold": 0}]}, "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}], "extensions": [], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "

The answer is a comma-separated list of numbers.

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The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.

", "name": "bits", "definition": "filter(x<>\"\",x,split(studentAnswer,\",\"))"}, {"description": "", "name": "expected_numbers", "definition": "settings[\"correctAnswer\"]"}, {"description": "

Is every number in the student's list valid?

", "name": "valid_numbers", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n true,\n let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n warn(wrong+\" is not a valid number\");\n fail(wrong+\" is not a valid number.\")\n )\n )"}, {"description": "

Are the student's answers in ascending order?