No questions found
(a) Write 32 652
(i) correct to the nearest 10,
Answer(a)(i) .............................................................[1]
(ii) correct to the nearest 100.
Answer(a)(ii) ...........................................................[1]
(b) Write 62.584 correct to 1 decimal place.
Answer(b) .................................................................[1]
(c) Calculate $4.8^{4}$.
Answer(c) .................................................................[1]
(d) Find $\sqrt[3]{216}$.
Answer(d) .................................................................[1]
(e) Find the highest common factor (HCF) of 18 and 45.
Answer(e) .................................................................[1]
(f) Find the lowest common multiple (LCM) of 6 and 8.
Answer(f) .................................................................[1]
(g) Divide 442 in the ratio 8 : 9.
Answer(g) ................................. : .................................[2]
(h) Sem buys 7 hamburgers each costing $1.20.
Find how much change he receives from $10.
Answer(h) $ .................................................................[2]
557
589
581
(a) Write 0.75 as a fraction.
Answer(a) .............................[1]
(b) Write $\frac{2}{3}$ as a percentage, giving your answer correct to 4 significant figures.
Answer(b) .............................\% [2]
(c) Write 48\% as a fraction in its lowest terms.
Answer(c) .............................[2]
(d) Find 8\% of 72.
Answer(d) .............................[1]
(e) The price of a jacket is $\$96$.
The price is reduced by 20\%.
Find the new price of the jacket.
Answer(e) \$ .............................[2]
(f) $800 is invested for 5 years at 3\% per year simple interest.
Find the total interest received at the end of the 5 years.
Answer(f) \$ .............................[2]
590
513
556
A special die has 10 faces numbered 1 to 10. When the die is rolled it is equally likely to land on any face.
Find the probability that the die lands on
(a) an even number,
Answer(a) ............................................................... [1]
(b) a prime number,
Answer(b) ............................................................... [1]
(c) 11,
Answer(c) ............................................................... [1]
(d) a square number less than 5.
Answer(d) ............................................................... [1]
513
554
582
Jacinta asks some students in her class which colour they prefer. The results are in the table.
[Table_1:
Colour | Number of students
Brown | 1
Green | 4
Black | 8
Pink | 12
Blue | 15]
(a) Calculate the total number of students.
Answer(a) .................................................... [1]
(b) Write down the most popular colour.
Answer(b) .................................................... [1]
(c) Jacinta wants to draw a pie chart for these results.
[Table_2:
Colour | Number of students | Sector angle in pie chart
Brown | 1 |
Green | 4 |
Black | 8 |
Pink | 12 | 108°
Blue | 15 | 135°]
(i) Complete the table.
[2]
(ii) Complete the pie chart to show this information. Two sectors have been drawn for you.
[2]
533
535
500
HanRa asked 30 students if they ate cereal $(C)$ or toast $(T)$ for breakfast. The information is shown in the Venn diagram.
Write down the number of students in
(a) $C \cap T$, Answer(a) ............................................................. [1]
(b) $C$, Answer(b) ............................................................. [1]
(c) $(C \cup T)'$, Answer(c) ............................................................. [1]
(d) $T \cup C'$. Answer(d) ............................................................. [1]
551
547
520
A trophy is in the shape of a cube of side 10 cm with a sphere of radius 5 cm on top.
(a) Find the surface area of the cube.
Answer(a) ....................................................... cm$^2$ [2]
(b) Find the surface area of the sphere.
Answer(b) ....................................................... cm$^2$ [2]
(c) Find the total \textbf{volume} of the trophy.
Answer(c) ....................................................... cm$^3$ [4]
The trophy is made from metal that costs 4 cents per cm$^3$.
(d) Find the cost of the metal used to make the trophy.
Give your answer in dollars.
Answer(d) $ ....................................................... [2]
581
565
508
The diagram shows a triangle $ABC$ and a trapezium $CDEF$.
$BCGD$ is a straight line and angle $FCD = 45^\circ$.
$AB = 36 \text{ cm}$, $BC = 12 \text{ cm}$, $CD = 31 \text{ cm}$ and $ED = 18 \text{ cm}$.
(a) Find the size of angle $CFE$.
Answer(a) Angle $CFE = \text{............................................................}$ [1]
(b) Use trigonometry to calculate the size of angle $BCA$.
Answer(b) Angle $BCA = \text{............................................................}$ [2]
(c) Use Pythagoras’ Theorem to find the length of $AC$.
Answer(c) $AC = \text{.................................................................}$ cm [2]
(d) Use trigonometry to calculate the length of $CF$.
Answer(d) $CF = \text{.................................................................}$ cm [3]
(e) (i) Explain why $EF = 13 \text{ cm}$.
[2]
(ii) Find the total perimeter of the shape.
Answer(e)(ii) \text{.................................................................}$ cm [1]
(f) Calculate the total area of the shape.
Answer(f) \text{.................................................................}$ cm$^2$ [3]
596
549
525
The table shows the number of shirts and the number of jackets owned by 12 students.
[Table_1]
(a) Complete the scatter diagram. The first 6 points have been plotted for you.
(b) Write down the type of correlation shown by the scatter diagram.
Answer(b) ...........................................................[1]
(c) (i) Find the mean number of shirts.
Answer(c)(i) ...........................................................[1]
(ii) Find the mean number of jackets.
Answer(c)(ii) ...........................................................[1]
(iii) On the diagram, plot the mean point. [1]
(d) On the diagram, draw a line of best fit by eye. [2]
(e) Use your line of best fit to estimate the number of jackets for a student who has 7 shirts.
Answer(e) ...........................................................[1]
521
558
523
(a) On the diagram, sketch the graph of $y = f(x)$ for $-3 \leq x \leq 1$. [2]
(b) Write down the $y$ co-ordinate of the point where the graph crosses the $y$-axis.
Answer(b) $y =$ ......................................................... [1]
(c) Write down the $x$ co-ordinates of the points where the graph crosses the $x$-axis.
Answer(c) $x =$ .......................... and $x =$ .......................... [2]
(d) Find the co-ordinates of the local maximum point.
Answer(d) $($ .......................... , .......................... $)$ [1]
(e) $g(x) = 2x + 4$
On the same diagram, sketch the graph of $y = g(x)$. [2]
(f) Find the co-ordinates of the points of intersection of $f(x)$ and $g(x)$.
Answer(f) $( .................. , .................. )$ and $( .................. , .................. )$ [2]
530
565
583
(a) Solve.
(i) $5x + 6 = -4$
Answer(a)(i) \text{................ [2]}
(ii) $6x + 3 < 21$
Answer(a)(ii) \text{................ [2]}
(b) Simplify.
(i) $s^3 \times s^4$
Answer(b)(i) \text{................ [1]}
(ii) $(t^2)^4$
Answer(b)(ii) \text{................ [1]}
(iii) $18r^3 \div 3r$
Answer(b)(iii) \text{................ [2]}
(c) Expand and simplify.
$4(x - 3) + 3(2x + 1)$
Answer(c) \text{................ [2]}
(d) Factorise completely.
$15y - 3y^2$
Answer(d) \text{................ [2]}
530
596
518
(a) Ahmed cycles 15 kilometres in 50 minutes. Find his average speed in kilometres per hour. Answer(a) .......................... km/h [3]
(b) George runs 15 kilometres at an average speed of 12 kilometres per hour. Find how many minutes it takes George to run the 15 kilometres. Answer(b) .......................... min [3]
525
571
519
