No questions found
(a) In 1911 the men's world record for the triple jump was 15.52 m.
In 2021 the record was 18.29 m.
Find 15.52 m as a percentage of 18.29 m.
............................................. % [1]
(b) In 2021 the women's world record for running 800 m was 1 minute 53 seconds.
Find the average speed for this run in m/s.
............................................. m/s [2]
(c) In 2021 the men's world record speed for running 100 m was 37.58 km/h.
Find the time taken, in seconds, for this run.
............................................. s [3]
595
577
546
These are Sunni’s last 12 scores in a game.
7 17 4 20 15 12 11 16 6 18 9 20
(a) Find
(i) the mode ...................................................... [1]
(ii) the median ...................................................... [1]
(iii) the mean ...................................................... [1]
(iv) the range ...................................................... [1]
(v) the upper quartile. ...................................................... [1]
(b) Explain why the mode is not the best measure of average to represent Sunni’s scores.
.....................................................................................................................................................
..................................................................................................................................................... [1]
587
513
525
(a) Translate triangle $A$ by the vector $\begin{pmatrix} -5 \\ 2 \end{pmatrix}$. Label the image $B$. [2]
(b) Describe fully the single transformation that maps triangle $A$ onto triangle $C$. [3]
(c) (i) Triangle $D$ is the image of triangle $A$ after a reflection in the line $y=-1$ followed by a rotation, $90^\circ$ clockwise, about the point $(1, -1)$.
Draw and label triangle $D$. [4]
(ii) Describe fully the single transformation that maps triangle $A$ onto triangle $D$. [2]
549
566
596
f(x) = 2x^3 - 3x^2 - 12x + 7 \text{ for } -3 \leq x \leq 4
(a) Sketch the graph of $y = f(x)$. [2]
(b) Solve $f(x) = 0$. ............................................................................................................................................................................................. [3]
(c) Find the values of $k$ for which $f(x) = k$ has exactly two solutions.
$k = \text{.............................. or } k = \text{..............................}$ [2]
(d) Find the range of values of $x$ for which the gradient of $f(x)$ is negative. ........................................................ [2]
555
515
543
A museum records the value of a picture every 5 years. The picture increases in value by 60\% every 5 years. The value the museum recorded in 2020 was \$20\,000.
(a) Calculate the value recorded in 2015.
$\$ \text{............................................}$ \quad [2]
(b) Show that the value recorded in 2040 will be \$131\,072.
[1]
(c) Calculate the year in which the value recorded will first be over \$1\,000\,000.
\text{............................................} \quad [4]
536
548
549
VABCD is a square-based pyramid. V is vertically above the centre of the base O. AD = 10 \text{cm} and VO = 12 \text{cm}.
(a) (i) Calculate the volume of the pyramid.
....................................... \text{cm}^3 [2]
(ii) M is the mid-point of CD. Show that VM = 13 \text{cm}.
[2]
A pyramid VPQRS is cut from the larger pyramid so that the face PQRS is parallel to the face ABCD. QR = 8 \text{cm}.
(b) (i) Calculate the volume of the remaining solid, ABCDPQRS.
....................................... \text{cm}^3 [4]
(ii) Calculate the total surface area of the remaining solid.
....................................... \text{cm}^2 [4]
532
564
538
240 people take part in a marathon race.
The times, $t$ minutes, they took for the race are shown in the cumulative frequency curve.
(a) Use the curve to estimate
(i) the median time ......................................... min [1]
(ii) the interquartile range. ......................................... min [2]
(b) The fastest 20\% of the runners are awarded a medal.
Use the curve to estimate the longest time taken by a runner who received a medal.
......................................... min [2]
(c) Use the curve to complete the frequency table.
[Table_1]
(d) Use the table in part (c) to calculate an estimate of the mean time.
......................................... min [2]
515
567
553
(a) $v = u + at$
Find $v$ when $u = 60$, $a = -32$ and $t = 3$.
$v = \text{.................................}$ [2]
(b) Solve.
(i) $6x + 2 = 9 - 4x$
$x = \text{.................................}$ [2]
(ii) $|2x - 3| = 7$
$\text{...........................................}$ [3]
(c) Solve by factorisation.
$3x^2 - 11x + 6 = 0$
$x = \text{......................... or } x = \text{.........................}$ [2]
(d) Rearrange $y = \frac{ax + 3b}{5x}$ to make $x$ the subject.
$x = \text{...............................}$ [3]
(e) Simplify.
$\frac{ax - 2bx + 3ay - 6by}{x^2 - 9y^2}$
$\text{...........................................}$ [4]
543
512
571
(a) For each Venn diagram, shade the given set.
[Image_1: U, A ∩ B]
[Image_2: U, P' ∪ Q']
(b) There are 120 students in a year group. The Venn diagram below shows the number of students who study History (H), Geography (G) and Economics (E).
[Image_3: Venn Diagram]
(i) Find the value of x. ............................................ [1]
(ii) One of the 120 students is chosen at random.
Find the probability that this student studies both History and Geography. ............................................ [1]
(iii) Two of the students who study Economics are chosen at random.
Find the probability that one of these students also studies Geography but not History and the other student also studies History but not Geography. ............................................ [3]
(iv) Three of the 120 students are chosen at random.
Find the probability that two students study exactly two of the subjects and the other student studies all three subjects. ............................................ [3]
514
591
505
(a) (i) Find $g(-3)$.
......................................................... [1]
(ii) Find $f(h(4))$.
........................................................ [2]
(iii) Find $g(f(x))$.
Give your answer in its simplest form.
........................................................ [2]
(iv) Find $h^{-1}(x)$.
$h^{-1}(x)=$ ........................................................ [2]
(b) (i) Sketch the graph of $y=\frac{f(x)}{g(x)}$ for values of $x$ between $-2$ and $4$.
[3]
(ii) Write down the equation of the asymptote which is parallel to the $y$-axis.
........................................................ [1]
(iii) Use the graph to solve $h(x)=\frac{f(x)}{g(x)}$.
$x=$ ........................... or $x=$ ........................... [3]
(iv) $h(x)=\frac{f(x)}{g(x)}$ can be rearranged to the form $ax^2+bx+c=0$.
Find the value of $a$, the value of $b$ and the value of $c$.
$a=$ .........................................................
$b=$ .........................................................
$c=$ ........................................................ [3]
525
595
510
(a) Calculate the value of $p$.
$p =$ .................................................. [2]
(b)
(i) Show that angle $ABC = 67.0^\circ$ correct to 1 decimal place.
(ii) Calculate the shortest distance from $A$ to the side $BC$.
............................................... m [3]
Total for Question: 9 marks
541
538
581
(a) Find the coordinates of the point where the line $y = 3x + 7$ crosses
(i) the $y$-axis
(...................... , ...................... ) [1]
(ii) the line $y = 2$.
(...................... , ...................... ) [2]
(b) $A$ is the point $(-5, 8)$ and $B$ is the point $(1, -2)$.
Find the equation of the perpendicular bisector of $AB$.
.................................................... [5]
597
556
597
