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Question1

Work out the number of months in 5 years.

▶️Answer/Explanation

60

Question2

Write 3752 correct to the

(a) nearest 10

(b) nearest 100.

▶️Answer/Explanation

(a) 3750 cao

(b) 3800 cao

Question3

Magazines cost $3.40 each.

Rosina has $15 to buy as many magazines as possible.

Complete the statement.

Rosina can buy …………….. magazines and will have $ …………….. left.

▶️Answer/Explanation

4 1.4[0]

Question4

Write down the mathematical name of a 4-sided shape that has rotational symmetry of order 2 and

no lines of symmetry.

▶️Answer/Explanation

Parallelogram

Question5

21                8              15             32            3             29             19           45          8
Calculate the mean of these numbers.

▶️Answer/Explanation

20

Question6

A train journey starts at 21 : 43.
It takes 8 hours and 32 minutes.
Find the time the journey finishes.

▶️Answer/Explanation

06 15 or 6:15am

Question7

Write these numbers in order, starting with the smallest.
$\frac{15}{213}$    0.071    0.7           7%

……………………. < ……………………. < ………………….. < …………………….

smallest

▶️Answer/Explanation

$7 \% \quad \frac{15}{213} \quad 0.071 \quad 0.7$

 

Question8

Write the fraction $\frac{24}{84}$ in its simplest form.

▶️Answer/Explanation

$\frac{2}{7}$

Question9

Simplify.

$3a-5b-a-6b$

▶️Answer/Explanation

$2a – 11b$

Question10

The cost of hiring a bicycle, $\$C$, for y hours is given by the formula $C=12+3.5y.$

Maria pays $\$36.50$ to hire this bicycle. Work out the number of hours she hires the bicycle for.

▶️Answer/Explanation

7

Question11

$a=\binom{3}{7}$             $b=\binom{-2}{5}$

Work out a-2b

▶️Answer/Explanation

$\binom{7}{-3}$   

Question12

(a) The diagram shows a pair of parallel lines and a straight line.
Write down the geometrical reason why the value of x is 52.

(b) Find the value of y and write down the geometrical reason for your answer.

▶️Answer/Explanation

(a) Alternate angles

(b) 196
Angles at a point sum to 360

 

Question13

Calculate the volume of a sphere with diameter 4.8cm.
[The volume, V, of a sphere with radius r is $V=\frac{4}{3}\pi r^3$]

▶️Answer/Explanation

57.9 or 57.90 to 57.91….

Question14

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the
value of

 $\frac{6.7 \times 2.1}{18-5.9}$

▶️Answer/Explanation

 $\frac{7 \times 2}{20-6}$

 

Question15

Eric has four colours of paint.
The table shows the probability that he uses each colour.

Find the value of x.

▶️Answer/Explanation

0.22 oe

Question16

Factorise completely.

$8x^2-20x$

▶️Answer/Explanation

4x(2x – 5)

Question17

(a) The nth term of a sequence is $10-n^2$

Write down the first three terms of this sequence.

(b) These are the first four terms of another sequence.
        7            10             13              16
Find an expression for the nth term of this sequence.

▶️Answer/Explanation

(a) 9 6 1

(b) 3n + 4

Question18

The length, l metres, of a piece of wood is 3.6 metres, correct to the nearest 10 centimetres.

Complete this statement about the value of l.

▶️Answer/Explanation

3.55 3.65

Question19

Calculate $1\div (6.4 \times 10^{-5})$
Give your answer in standard form.

▶️Answer/Explanation

$1.5625 × 10^4$

 

(b)

Shape drawn correctly

Question20

Without using a calculator, work out

$2\frac{1}{7}\div \frac{5}{9}$

You must show all your working and give your answer as a mixed number in its simplest form.

▶️Answer/Explanation

$\frac{15}{7} \times \frac{9}{5}$

Question21

The diagram shows a right-angled triangle.
Use the information in the diagram to write down and solve an equation to find the value of x.

▶️Answer/Explanation

$4x + 3x – 1 + 90 = 180$

Question22

The diagram shows a right-angled triangle.
Calculate the value of y.

▶️Answer/Explanation

30.4 or 30.36 to 30.37

Question23

Triangle ABC is similar to triangle DEF.

Calculate the value of h.

▶️Answer/Explanation

$6.3$

Question24

$$
\begin{aligned}
& \mathscr{E}=\{\mathrm{a}, \mathrm{~b}, \mathrm{c}, \mathrm{~d}, \mathrm{e}, \mathrm{f}, \mathrm{~g}, \mathrm{~h}, \mathrm{i}, \mathrm{j}, \mathrm{k}\} \\
& F=\{\mathrm{f}, \mathrm{a}, \mathrm{c}, \mathrm{e}\} \\
& B=\{\mathrm{b}, \mathrm{a}, \mathrm{c}, \mathrm{k}\}
\end{aligned}
$$

(a) Complete the Venn diagram.


(b) Find $\mathrm{n}(F \cup B)$.

▶️Answer/Explanation

(b) 6

Question25

At a cinema, an adult ticket costs $\$a$ and a child ticket costs $\$c$.

(a) Farah buys 3 adult tickets and 4 child tickets for $\$38.50$ .

Complete the equation.

$3a + 4c =$ ?

(b) Hana buys $6$ adult tickets and $5$ child tickets for $\$65.00$ .

Write down another equation in terms of a and c.

(c) Solve the two simultaneous equations to find the value of a and the value of c.

You must show all your working.

▶️Answer/Explanation

(a) 38.5

(b) 6a + 5c = 65

(c) Correctly eliminating one variable 
[a =] 7.5 
[c =] 4

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