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Which of the following are true and which are false? There are 20 marks available. Each error will cost 4 marks.

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15 questions based on module so far.

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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.

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