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Question1

(a) Write down all the factors of $18.$

(b) Write down the reciprocal of $8.$

▶️Answer/Explanation

(a): $1, 2, 3, 6, 9, 18$

(b): $\frac{1}{8}$ or $0.125$

Question2

(a) Draw a line perpendicular to the line AB. 
(b) Measure the line AB in centimetres.

▶️Answer/Explanation

(a): Accurate ruled perpendicular line

(b): $7.4$

Question3

Shade two squares so that the diagram has rotational symmetry of order $4.$

▶️Answer/Explanation

Question4

 Kai and Ava each have a piece of wood $57$cm long.
(a) Kai cuts his piece into $4$ equal length parts.
Find the length of one part.

(b) Ava cuts her piece into two parts and the lengths are in the ratio $5 :1 $.
Find the length of the longer part.

▶️Answer/Explanation

(a): $14.25$

(b): $47.5$

Question5

In the diagram, $ABC$ is a triangle and $ACD$ is a straight line.
Find the value of $x$ and the value of $y.$

▶️Answer/Explanation

$x = 48$, $y = 132$

Question6

Find the temperature that is $8°C$ colder than $-5°C$.

▶️Answer/Explanation

$-13$

Question7

There are two prime numbers in this list.

$27\quad47\quad57\quad61\quad75\quad93$

Work out the sum of these two prime numbers.

▶️Answer/Explanation

$108$

Question8

On ten days, Stefan records the number of minutes he has to wait for a train.

$1\quad3\quad12\quad5\quad4\quad23\quad5\quad24\quad11\quad8$

(a) Complete the stem-and-leaf diagram to show this information.

(b) Find the median.

▶️Answer/Explanation

(a)

(b): $6.5$ 

Question9

 The scale drawing shows the positions of town $A$ and town $B.$

Measure the bearing of town $B$ from town $A$.

▶️Answer/Explanation

 $135$

Question10

 

The diagram shows a right-angled triangular prism.

On the $l$ cm$^{2}$ grid, complete the net of this prism.
One face has been drawn for you.

▶️Answer/Explanation

 Fully correct net

Question11

The distance from town $A$ to town $B$ on a map is $3.5$cm.
The scale on the map is $1 : 250 000$.
Find the actual distance, in kilometres, from town $A$ to town $B.$

▶️Answer/Explanation

 $8.75$

Question12

 A spinner is spun. The possible outcomes are A, B, C or D.
The probability of spinning A, C or D is shown in the table.

Complete the table.

▶️Answer/Explanation

$0.4$

Question13

$\mathcal{E}=\{x:1\leqslant x\leqslant20\}$

$E=\{$even numbers$\}$

$M=\{$multiples of 5$\}$

$(\mathbf{a})$ Find n$(M).$

$(\mathbf{b})$ Find the elements in the set $E\cap M.$

▶️Answer/Explanation

(a): $4$

(b): $10, 20$

Question14

Without using a calculator, work out $\frac{4}{7}\div1\frac{5}{21}$
You must show all your working and give your answer as a fraction in its simplest form.

▶️Answer/Explanation

$\frac{4}{7} \times \frac{21}{26}$ or $\frac{12}{21} \div \frac{26}{21}$ (with common denominator). $\frac{6}{13}$

Question15

$F$ is the point $(1,-4),$ $\overrightarrow{FG} = \begin{pmatrix} 8\\ – 3\end{pmatrix}$and $\overrightarrow {GH}=\begin{pmatrix}-12\\35\end{pmatrix}.$

Find

$(\mathbf{a})$ $3\overrightarrow{FG}$

$( \mathbf{b} )$ $\overrightarrow {FG}+ \overrightarrow {GH}$

$( \mathbf{c} )$ the coordinates of the point $G.$

▶️Answer/Explanation

(a): $\begin{pmatrix} 24 \\ -9 \end{pmatrix}$

(b): $\begin{pmatrix} -4 \\ 32 \end{pmatrix}$

(c): $(9, -7)$

Question16

16 $x$ is an integer where $x\geqslant-3$ and $x<3.$
Write down all the possible values of $x$

▶️Answer/Explanation

$-3, -2, -1, 0, 1, 2$

Question17

 Find the size of an interior angle of a regular $15-$sided polygon

▶️Answer/Explanation

$156$

Question18

(a) Write $45 000$ in standard form

(b) Calculate $6.75\times10^{-3}\times4.2\times10^{5}$
Give your answer in standard form.

▶️Answer/Explanation

(a): $4.5 \times 10^4$

(b): $2.835 \times 10^3$

Question19

 Simplify. $18x^{12}\div3x^3$

▶️Answer/Explanation

$6x^9$

Question20

\(\begin{aligned}&\text{Buses at a station go to the port or to the town.}\\&\text{Buses leave every 28 minutes for the port.}\\&\text{Buses leave every 48 minutes for the town leave the station together.}\\&\text{Find the next time when a bus for the port and a bus for the town leave the station together.}\end{aligned}\)

▶️Answer/Explanation

$1554$ or $3:54$ pm

Question21

Triangle $ABC$ is similar to triangle $PQR.$
Calculate $QR.$

▶️Answer/Explanation

$10.8$

Question22

(a) 

The diagram shows a right-angled triangle $ABC.$
Calculate $AB.$

(b) 

The diagram shows right-angled triangles $PQS$ and $PRS.$
$PQ=23.8$cm$, $QS=11.2~cm~ and ~SR=20cm$.

Calculate $PR.$

▶️Answer/Explanation

(a): $5.75$ or $5.754$ to $5.755$

(b): $29$

Question23

$( \mathbf{a} )$ The mass, $m$ kilograms, of object $A$ is $350$kg, correct to the nearest 10 kg.
Complete this statement about the value of $m.$

$\mathbf{(b)}$ The mass of object $B$ is $348$ kg, correct to the nearest kilogram.
Show that the mass of object $B$ may be more than the mass of object $A.$

▶️Answer/Explanation

(a): $345$, $355$

(b): Any correct response e.g. A could be $345$

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