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Question1

(a) Complete the statement.

The diagram has rotational symmetry of order

(b) On the diagram, draw all the lines of symmetry.

▶️Answer/Explanation

(a): $2$

(b)

Question2

A film lasts for 2 hours 50 minutes.
The film ends at 23 05.
Find the time the film starts.

▶️Answer/Explanation

 $20\ 15$ or $8:15$ pm

Question3

Find the total surface area of the cuboid.

▶️Answer/Explanation

$158$

Question4

$$\nu=u-9.8t$$

Find the value of $\nu$ when $u= 4$ and $t= – 7.$

▶️Answer/Explanation

 $72.6$

Question5

Simplify $d^8\div d^2.$

▶️Answer/Explanation

$d^6$

Question6

At the end of the day, a shopkeeper has 12 tins of cat food left This is $\frac{3}{13}$ of the number he had at the beginning of the day Calculate the number of tins he had at the beginning of the day

▶️Answer/Explanation

 $52$

Question7

A spinner has five sides.
Each side is painted red, blue, green, yellow or orange.
The table shows some of the probabilities of the spinner landing on each colour.

(a) Complete the table. 
(b) Dan spins the spinner once.
Find the probability that the spinner lands on red or blue.

▶️Answer/Explanation

(a): $0.11$

(b): $0.46$

Question8

Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

▶️Answer/Explanation

 Rotation, $(0,0)$, $90^\circ$ clockwise

Question9

The distance–time graph shows information about Kai’s journey from home to the office.

(a) Calculate the average speed, in km/h, for Kai’s journey from home to the office.

(b) When Kai arrives at the office, he finds his meeting is cancelled. He immediately returns home at a constant speed of $50$km/h.
Complete the distance–time graph to show his journey home.

▶️Answer/Explanation

(a): $32.5$

(b): Correct ruled line from $(1200, 65)$ to $(1318, 0)$

Question10

Without using a calculator, work out 5$\frac {11}{12}+ 2\frac 14$ .

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

▶️Answer/Explanation

 $\frac{k}{12} + \frac{27}{12}$ or $\frac{71}{12} + \frac{c}{12}$. $[5]\frac{11}{12}$ and $[2]\frac{3}{12}$. $8\frac{1}{6}$

Question11

(a)\(\begin{aligned}\mathrm{(a)}&\varepsilon=\{a,b,e,g,l,m,o,r,t,y\}\\&P=\{a,b,e,g,l,r\}\\&Q=\{e,g,m,o,r,t,y\}\end{aligned}\)

 

Complete the Venn diagram.

(b)

\(\text{Shade the region}~A^{\prime}\cap B.\)

▶️Answer/Explanation

Question12

12 The position vector of $A$ is$\binom {5}{3} $and $\overrightarrow{BA}=\binom {4}{8}$
Show that $\left|\overrightarrow{OB}\right|=5.1$, correct to 1 decimal place

▶️Answer/Explanation

$\sqrt{1^2 + (-5)^2}$.

Question13

Calculate $\sqrt{42}+3^{0.4}$

▶️Answer/Explanation

 $8.03$ or $8.032$ to $8.033$

Question14

Write $0.581$ as a fraction.
You must show all your working and give your answer in its simplest form

▶️Answer/Explanation

 $581.81… – 5.81…$ which simplifies to $\frac{32}{55}$

Question15

The number of trees in a forest is decreasing exponentially at a rate of $1.75\%$ per year
Eleven years ago there were $980$ trees

Calculate the number of trees in the forest now Give your answer correct to the nearest integer.

▶️Answer/Explanation

$807$

Question16

The volume of a cylinder is $1970$ cm$^{3}$ The height of the cylinder is $12.8$cm. Calculate the radius of the cylinder.

▶️Answer/Explanation

$7.00$ or $6.998$ to $7.002$

Question17

Rearrange the formula to make $m$ the subject.

$$R=\frac{2(m-k)}m$$

▶️Answer/Explanation

$m = \frac{2k}{(2-R)}$ or $m = \frac{-2k}{(R-2)}$

Question18

$y$ is inversely proportional to the cube root of $(x+5).$
${\mathrm{When~}x=3,y=12.}$

Find $y$ when $x=22.$

▶️Answer/Explanation

$8$

Question19

\(\begin{aligned}&\text{Solve the equation}\quad x^2+5x-7=0.\\&\text{You must show all your working and give your answers correct to 2 decimal places.}\end{aligned}\)

▶️Answer/Explanation

 $\frac{-5 \pm \sqrt{5^2 – 4 \times 1 \times -7}}{2 \times 1}$. $-6.14$ and $1.14$

Question20

$$\mathrm{f}(x)=6x-7\quad\mathrm{g}(x)=x^{-3}$$

$( \mathbf{a} )$ Find f$(x+2).$

Give your answer in its simplest form.

$( \mathbf{b} )$ Find f$^{- 1}( x)$ .

$( \mathbf{c} )$ Find $x$ when g$(x)=$f(22).

▶️Answer/Explanation

(a): $6x + 5$

(b): $\frac{x+7}{6}$ or $\frac{x}{6} + \frac{7}{6}$

(c): $\frac{1}{5}$ or $0.2$

Question21

Simplify.

$$\frac{2x^2+5x-12}{4x^2-9}$$

▶️Answer/Explanation

 $\frac{x+4}{2x+3}$

Question22

These are the first four terms of a sequence

$2.75\quad6\quad11.25\quad20$

The $n$th term of this sequence is $\frac{1}{4}n^3+an^2+bn.$

Calculate the value of $a$ and the value of $b.$

▶️Answer/Explanation

 $a = \frac{1}{2}$, $b = 3$

Question23

A train travels between two stations.
The distance between the stations is $220$ km, correct to the nearest kilometre.
The speed of the train is $125$ km/h, correct to the nearest $5$ km/h.
Calculate the upper bound for the time the journey takes.
Give your answer in hours and minutes.

▶️Answer/Explanation

$1$h $48$ min

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