True

", "False

"], "shuffleChoices": true, "prompt": "Which of the following are true and which are false? There are 20 marks available. Each error will cost 4 marks.

", "showFeedbackIcon": true, "marks": 0, "maxAnswers": 0, "choices": "{statements}", "displayType": "radiogroup", "variableReplacements": []}], "name": "Maths 1. True false", "metadata": {"description": "15 questions based on module so far.

", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "variables": {"rand2": {"description": "", "definition": "shuffle(map(j,j,0..78))", "group": "do not change these", "templateType": "anything", "name": "rand2"}, "rand": {"description": "", "definition": "repeat(random(0..1),n)", "group": "do not change these", "templateType": "anything", "name": "rand"}, "n": {"description": "", "definition": "50", "group": "change these", "templateType": "anything", "name": "n"}, "marks": {"description": "", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-3.6],[-3.6,max_mark/n]),j,0..n-1))\n", "group": "do not change these", "templateType": "anything", "name": "marks"}, "statements_false": {"description": "", "definition": "[\"Solving an equation means finding the answer\",\n \"To divide by a fraction, you need to make the denominators equal first\",\n \"Dividing by $\\\\frac{1}{7}$ is the same as multiplying by $\\\\frac{1}{7}$\",\n \"The circumference of a circle of radius $r$ is $\\\\pi r$\",\n \"Dividing by $0.01$ is the same as dividing by $100$\",\n\"To get from $\\\\var{a}^{\\\\var{b}}$ to $\\\\var{a}^{\\\\var{b+1}}$, you add $1$\",\n \"$\\\\log_2(8) = 3$ because that's what the calculator says\",\n \"$-\\\\var{c}^2$ equals $\\\\var{c^2}$\",\n \"$\\\\sqrt{\\\\var{(c-1)^2}}$ equals $\\\\var{c-1}$ or $-\\\\var{c-1}$\",\n \"$a(b+c) \\\\neq ab+ac$\",\n \"$\\\\sin(b+c) = \\\\sin(b) + \\\\sin(c) $\",\n \"$\\\\sqrt{b+c} = \\\\sqrt{b} + \\\\sqrt{c}$\",\n \"$(b+c)^4 = b^4 + c^4$\",\n \"$\\\\frac{b+c}{a} \\\\neq \\\\frac{b}{a} + \\\\frac{c}{a}$\",\n \"$\\\\frac{a}{b+c} = \\\\frac{a}{b} + \\\\frac{a}{c}$\",\n \"$\\\\sin(\\\\theta)$ can be bigger than $1$\",\n \"$\\\\tan(\\\\theta)$ can never be bigger than $1$\",\n \"If $0<\\\\theta<45^{\\\\circ}$, then the length of the opposite of the angle is larger than the adjacent.\",\n \"$\\\\Delta L$ means triangle $L$\",\n \"A solution of an equation is an answer of the equation\",\n \"Increasing $X$ by $3\\\\%$ is the same as adding $3$ to $X$\",\n \"In the context of coordinates, $O$ represents zero\",\n \"When handwritten, a variable representing a vector should be drawn with bold font\",\n \"$\\\\vec{AB}$ is the distance between $A$ and $B$\",\n \"If $45<\\\\theta<90^{\\\\circ}$ in a right-angled triangle, then the length of the opposite of the angle is smaller than the adjacent.\",\n\"If the discriminant of a quadratic equation is 0, the equation has zero solutions\",\n \"In a quadratic, if the coefficient of the squared term is negative, then the graph of the quadratic will be convex\",\n \"A quadratic equation always has two solutions\",\n \"A precise definition of the gradient of a straight line is that it is the slope of the line\",\n \"The gradient of a straight line is $\\\\frac{\\\\Delta x}{\\\\Delta y}$ \",\n \"$\\\\tan(b+c) = \\\\tan(b) + \\\\tan(c) $\",\n \"A straight line has equation $y=-x+c$. This means the gradient is $1$\",\n \"After finishing a question, you should not waste time checking your answer\",\n \"If the discriminant of a quadratic equation is less than 0, the equation has two solutions\",\n\"If $f$ is a function, then $f(5)$ means $f \\\\times 5$\",\n\"$|-10| = -10$\",\n\"On the graph of a function $g$, if the $y$-coordinate is $7$, then the $x$-coordinate is $g(7)$\",\n\"$5^{a} \\\\times 5^{b} = 25^{ab}$\",\n\"$5^{a} \\\\div 5^{b} = 5^{a \\\\div b}$\",\n\"$5^{a \\\\times b} = 5^a \\\\times 5^b$ \",\n\"$5^0=0$ \",\n\"$5^1=1$\",\n\"$5^{-3}=-5^3$\",\n\"$5^{1/3} = \\\\frac{1}{5^3}$\",\n\"$\\\\log(a+b) = \\\\log(a)+\\\\log(b)$\",\n \"$\\\\log(ab) \\\\neq \\\\log(a) + \\\\log(b)$\",\n \"$\\\\log(a)-\\\\log(b) = \\\\log(a-b)$\",\n \"$-\\\\log(\\\\frac{a}{b}) \\\\neq \\\\log(\\\\frac{b}{a})$\",\n \"$\\\\frac{\\\\log(a)}{\\\\log(b)} = \\\\log_a(b)$\",\n \"$e^{a+b} = e^{a} + e^{b}$\",\n \"$(e^a)^b \\\\neq e^{ab}$\",\n \"$\\\\sin(0)=1 $\",\n \"$\\\\cos(0)=0 $\",\n \"$\\\\sin(\\\\pi)=-1$\",\n \"$\\\\cos(\\\\pi)=0 $\",\n \"$\\\\sin(\\\\frac{\\\\pi}{2})=0$\",\n \"$\\\\cos(\\\\frac{\\\\pi}{2})=1 $\",\n \"When finding an angle using the sine rule, there is nothing significant to watch out for\",\n\"If $f$ is a function, then $f^{-1}$ equals $\\\\frac{1}{f}$\",\n\"If $x$ is a number, then $x^{-1}$ equals $-x$\",\n\"$f(g(x))$ means first do $f$ and then do $g$\",\n\"When solving $\\\\sin(x)=0.1$, $\\\\sin^{-1}(0.1)$ gives you the answer\",\n\"To show you can add multiples of $2\\\\pi$, we write `$+2n\\\\pi$ where $n$ is any number' \",\n\"Trigonometric equations have only one solution\",\n\"If the gradient on a curve is $m$, then $\\\\Delta y = m \\\\Delta x$\",\n\"$\\\\delta x$ means `a change in $x$' \",\n\"$\\\\log(ab) = \\\\log(a)\\\\log(b)$\",\n\"$\\\\sin(ab) = \\\\sin(a) \\\\sin(b)$\",\n\"$\\\\sqrt{ab} = \\\\sqrt{a}+\\\\sqrt{b}$\",\n\"$\\\\dfrac{\\\\sqrt{a}}{b} = \\\\sqrt{\\\\dfrac{a}{b}}$\",\n\"'$ ^nC_r$' is pronounced '$n$-see-$r$ ' \",\n\"'$ n!$' is pronounced '$n$ exclamation mark ' \",\n\"$ \\\\dfrac{6!}{3!} = 2!$\",\n\"To get from a graph of $f(x)$ to a graph of $f(x)+3$, you translate right by 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(x+3)$, you translate up by 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(x-3)$, you translate left by 3\",\n\"To get from a graph of $f(x)$ to a graph of $3f(x)$, you stretch horizontally by a factor of 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(3x)$, you stretch horizontally by a factor of 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(\\\\frac{1}{3}x)$, you compress horizontally by a factor of 3\"\n]\n", "group": "change these", "templateType": "anything", "name": "statements_false"}, "a": {"description": "", "definition": "random(3..7)", "group": "change these", "templateType": "anything", "name": "a"}, "statements": {"description": "", "definition": "map(if(rand[j]=1,\n statements_true[rand2[j]],\n statements_false[rand2[j]]),j,0..n-1)", "group": "do not change these", "templateType": "anything", "name": "statements"}, "b": {"description": "", "definition": "random(10..18)+random(1..9)/10", "group": "change these", "templateType": "anything", "name": "b"}, "max_mark": {"description": "", "definition": "20", "group": "change these", "templateType": "anything", "name": "max_mark"}, "statements_true": {"description": "", "definition": "[\"Solving an equation means finding all values of the unknown which makes the equation true\",\n \"To divide by a fraction, you do not need to make the denominators equal first\",\n \"Dividing by $\\\\frac{1}{7}$ is the same as multiplying by $7$\",\n \"The circumference of a circle of radius $r$ is $2\\\\pi r$\",\n \"Dividing by $0.01$ is the same as multiplying by $100$\",\n\"To get from $\\\\var{a}^{\\\\var{b}}$ to $\\\\var{a}^{\\\\var{b+1}}$, you multiply by $\\\\var{a}$\",\n \"$\\\\log_2(8) = 3$ because $2^3=8$\",\n \"$-\\\\var{c}^2$ equals $-\\\\var{c^2}$\",\n \"$\\\\sqrt{\\\\var{(c-1)^2}}$ equals $\\\\var{c-1}$, not $-\\\\var{c-1}$\",\n \"$a(b+c)=ab+ac$\",\n \"$\\\\sin(b+c) \\\\neq \\\\sin(b) + \\\\sin(c) $\",\n \"$\\\\sqrt{b+c} \\\\neq \\\\sqrt{b} + \\\\sqrt{c}$\",\n \"$(b+c)^4 \\\\neq b^4 + c^4$\",\n \"$\\\\frac{b+c}{a} = \\\\frac{b}{a} + \\\\frac{c}{a}$\",\n \"$\\\\frac{a}{b+c} \\\\neq \\\\frac{a}{b} + \\\\frac{a}{c}$\",\n \"$\\\\sin(\\\\theta)$ can never be bigger than $1$\",\n \"$\\\\tan(\\\\theta)$ can be bigger than $1$\",\n \"If $0<\\\\theta<45^{\\\\circ}$, then the length of the opposite of the angle is shorter than the adjacent.\",\n \"$\\\\Delta L$ means the change in $L$\",\n \"A solution of an equation is a value of the unknown quantity that makes the equation true\",\n \"Increasing $X$ by $3\\\\%$ is the same as multiplying $X$ by $1.03$\",\n \"In the context of coordinates, $O$ represents the origin\",\n \"When handwritten, a variable representing a vector should be underlined or have an arrow above it\",\n \"$\\\\vec{AB}$ represents the vector joining $A$ to $B$\",\n \"If $45<\\\\theta<90^{\\\\circ}$ in a right-angled triangle, then the length of the opposite of the angle is larger than the adjacent.\",\n\"If the discriminant of a quadratic equation is 0, the equation has one solution\",\n \"In a quadratic, if the coefficient of the squared term is negative, then the graph of the quadratic will be concave\",\n \"A quadratic equation can have zero, one or two solutions\",\n \"The gradient of a straight line tells you how far you move up if you move to the right by 1\",\n \"The gradient of a straight line is $\\\\frac{\\\\Delta y}{\\\\Delta x}$ \",\n \"$\\\\tan(b+c) \\\\neq \\\\tan(b) + \\\\tan(c) $\",\n \"A straight line has equation $y=-x+c$. This means the gradient is $-1$\",\n \"After finishing a question, where possible, you should check your answer\",\n \"If the discriminant of a quadratic equation is less than 0, the equation has no solutions\",\n\"If $f$ is a function, then $f(5)$ represents the output of $f$ when you input $5$\",\n\"$|-10| = 10$\",\n\"On the graph of a function $g$, if the $x$-coordinate is $7$, then the $y$-coordinate is $g(7)$\",\n\"$5^{a} \\\\times 5^{b} = 5^{a+b}$\",\n\"$5^{a} \\\\div 5^{b} = 5^{a-b}$\",\n\"$5^{ab} = (5^{a})^{b}$ \",\n\"$5^0=1$ \",\n\"$5^1=5$\",\n\"$5^{-3}=\\\\frac{1}{5^3}$\",\n\"$5^{1/3} = \\\\sqrt[3]{5}$\",\n\"$\\\\log(a+b) \\\\neq \\\\log(a)+\\\\log(b)$\",\n \"$\\\\log(ab) = \\\\log(a)+\\\\log(b)$\",\n \"$\\\\log(a)-\\\\log(b) = \\\\log(\\\\frac{a}{b})$\",\n \"$-\\\\log(\\\\frac{a}{b}) = \\\\log(\\\\frac{b}{a})$\",\n \"$\\\\frac{\\\\log(a)}{\\\\log(b)} \\\\neq \\\\log(\\\\frac{a}{b})$\",\n \"$e^{a+b} \\\\neq e^{a} + e^{b}$\",\n \"$(e^a)^b = e^{ab}$\",\n \"$\\\\sin(0)=0 $\",\n \"$\\\\cos(0)=1 $\",\n \"$\\\\sin(\\\\pi)=0$\",\n \"$\\\\cos(\\\\pi)=-1 $\",\n \"$\\\\sin(\\\\frac{\\\\pi}{2})=1$\",\n \"$\\\\cos(\\\\frac{\\\\pi}{2})=0 $\",\n \"When finding an angle using the sine rule, you have to think about if the angle is bigger or smaller than $90^{\\\\circ}$\",\n\"If $f$ is a function, then $f^{-1}$ is the function that undoes $f$\",\n\"If $x$ is a number, then $x^{-1}$ equals $\\\\frac{1}{x}$\",\n\"$f(g(x))$ means first do $g$ and then do $f$\",\n\"When solving $\\\\sin(x)=0.1$, $\\\\sin^{-1}(0.1)$ gives you only one solution\",\n\"To show you can add multiples of $2\\\\pi$, we write `$+2n\\\\pi$ where $n$ is any whole number' \",\n\"Trigonometric equations have infinitely many solutions\",\n\"If the gradient on a curve is $m$, then $\\\\Delta y \\\\approx m \\\\Delta x$\",\n\"$\\\\delta x$ means `a small change in $x$' \",\n\"$\\\\log(ab) = \\\\log(a)+\\\\log(b)$\",\n\"$\\\\sin(ab) \\\\neq \\\\sin(a) \\\\sin(b)$\",\n\"$\\\\sqrt{ab} = \\\\sqrt{a}\\\\sqrt{b}$\",\n\"$\\\\dfrac{\\\\sqrt{a}}{b} = \\\\sqrt{\\\\dfrac{a}{b^2}}$\",\n\"'$ ^nC_r$' is pronounced '$n$ choose $r$ ' \",\n\"'$ n!$' is pronounced '$n$ factorial ' \",\n\"$ \\\\dfrac{6!}{3!} = 6 \\\\cdot 5 \\\\cdot 4$\",\n\"To get from a graph of $f(x)$ to a graph of $f(x)+3$, you translate up by 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(x+3)$, you translate left by 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(x-3)$, you translate right by 3\",\n\"To get from a graph of $f(x)$ to a graph of $3*f(x)$, you stretch vertically by a factor of 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(3x)$, you compress horizontally by a factor of 3\",\n\"To get from a graph of $f(x)$ to a graph of $f(\\\\frac{1}{3}x)$, you stretch horizontally by a factor of 3\"\n]\n", "group": "change these", "templateType": "anything", "name": "statements_true"}, "c": {"description": "", "definition": "random(6..9)", "group": "change these", "templateType": "anything", "name": "c"}}, "tags": [], "extensions": [], "advice": "See all the lectures and workshops up to this point.

", "statement": "This is a non-calculator question.

", "preamble": {"css": "", "js": ""}, "ungrouped_variables": [], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}