Question1
(a) $40$ football players vote on the colour of new shirts.
The results for red, yellow and green are shown in the bar chart.
(i) Twice as many football players vote blue than vote orange.
Complete the bar chart.
(ii) Write down the mode.
▶️Answer/Explanation
(a)(i): Correct bars at [blue] $10$ and [orange] $5$
(a)(ii): Red
(b)(i): Correct pie chart
(b)(ii): $30$
Question2
(a) Here is part of the timetable for buses from the station to the city centre.
All buses take the same time to travel from the station to the city centre.
(i) Complete the timetable.
(ii) Beth walks 4 km from her home to the station at a speed of 6km/h.
She wants to travel on the 0924 bus.
Work out the latest time she can leave her home.
(iii) 45 seats on the bus are occupied.
This is $\frac{3}{5}$ of the total number of seats on the bus.
Work out the total number of seats on the bus.
(b) Beth buys $2.4$kg of onions costing \(\$1.25\) per kilogram and $4.5$kg of potatoes.
The total cost is \(\$11.64\) .
Find the cost of $1$kg of potatoes.
$( \mathbf{c} )$ $( \mathbf{i} )$ One day 140 people enter a shop
The ratio \(\textbf{adults:children=3:2}\).
Find the number of adults who enter the shop
(ii) The price of a television in this shop is S624.
$37.5\%$ of this price is profit.
Calculate the profit on this television.
(iii) The price of a phone in this shop is \(\$420\).
This price increases by $12\%$.
Calculate the new price.
▶️Answer/Explanation
(a)(i): $1145$
(a)(ii): $0844$
(a)(iii): $75$
(b): $1.92$
(c)(i): $84$
(c)(ii): $234$
(c)(iii): $470.40$
Question3
(a) The grid shows a trapezium.
On the grid, draw an enlargement of the trapezium with scale factor $3. $
$\mathbf{( b) }$ The diagram shows four triangles, $A,B,C$ and $T$,and a point $P$ on a grid
(i) Write down the coordinates of point $P.$
(ii) Describe fully the single transformation that maps
(a) triangle $T$ onto triangle $A$
(b) triangle $T$ onto triangle $B$
(c) triangle $T$ onto triangle $C.$
▶️Answer/Explanation
(a): Correct enlargement
(b)(i): $4.3$
(b)(ii)(a): Reflection, $x = -1$
(b)(ii)(b): Translation $\begin{pmatrix} 3 \\ -5 \end{pmatrix}$
(b)(ii)(c): Rotation, $(0, 0)$, $180^\circ$
Question4
(a) Write down the value of the $8$ in the number $39829$
(b) Write down all the factors of $18$
(c) Show that 57 is not a prime number.
$(\mathbf{d})$
$$\sqrt{x}=64$$
Find the value of $x.$
$( \mathbf{e} )$ Find the first multiple of $40$ that is greater than 620
$( \mathbf{f} )$ Find the reciprocal of $\frac{2}{3}.$
\(\begin{aligned}&(\mathbf{g})\quad\text{Find a fraction between }\frac{1}{5}\mathrm{~and~}\frac{1}{4}.\\&(\mathbf{h})\quad\text{Write down an irrational number with a value between 9 and 10.}\\&&&\mathrm{…}\\&(\mathbf{i})\quad\mathrm{Find~the~highest~common~factor~(HCF)~of~72~and~180.}\end{aligned}\)
▶️Answer/Explanation
(a): $800$
(b): $1, 2, 3, 6, 9, 18$
(c): $57 = 3 \times 19$
(d): $4096$
(e): $640$
(f): $1\frac{1}{2}$ or $1.5$
(g): Any correct fraction
(h): Any correct irrational number
(i): $36$
Question5
(a) 
(i) Measure angle $k.$
(ii) Write down the mathematical name for this type of angle
$\mathbf{(b)}$ The diagram shows a pair of parallel lines and a straight line.
Angles $a,b,c,d$ and $x$ are labelled.
Complete the statements.
Angle ……………….. is alternate to angle x.
Angle ……………….. is corresponding to angle x.
(c) The diagram shows a parallelogram.
Find the value of y.
(d) 
$A,B$ and $C$ lie on a circle, centre $O.$
Find angle $ACB.$
$( \mathbf{e} )$ The interior angle of a regular polygon is 171°.
Work out the number of sides of this polygon.
$(\mathbf{f})$
Calculate the value of $x.$
▶️Answer/Explanation
(a)(i): $326$
(a)(ii): reflex
(b): $c$, $d$
(c): $138$
(d): $73^\circ$
(e): $40$
(f): $23.6$ or $23.57$ to $23.58$
Question6
(a) In a sport, teams are given points using the formula
number of points=number of wins$\times4+$number of draws$\times2+$bonus points
One team has 15 wins, 7 draws and 6 bonus points Calculate the total number of points for this team.
$(\mathbf{b})$ Solve. $\frac{ x}{2}= 18$
$(\mathbf{c})$ Solve.
$4x+12=18$
$( \mathbf{d} )$ Expand and simplify
$$6(3x-4)+5(x-2)$$
$(\mathbf{e})$
$$T=5r-6$$
Make $r$ the subject of this formula.
(f)
\(\begin{aligned}&\text{Bo has a green bag and a blue bag.}\\&\text{Each bag contains some marbles.}\\&\text{The green bag has x marbles.}\\&\text{There are 5 times as many marbles in the blue bag than in the green bag.}\\&\text{Bo now adds 6 marbles to each bag.}\\&\text{There are now 4 times as many marbles in the blue bag than in the green bag.}\\&\text{Use this information to write down an equation and sol sol te it to find the value of }x.\end{aligned}\)
▶️Answer/Explanation
(a): $80$
(b): $36$
(c): $1\frac{1}{2}$ or $1.5$
(d): $23x – 34$
(e): $r = \frac{T + 6}{5}$
(f): $5x + 6 = 4(x + 6)\Rightarrow x=18$
Question7
(a) Li spins a fair 6-sided spinner numbered $1$ to $6$.
On the probability scale, draw an arrow $(\downarrow )$ to show the probability that the spinner lands on he number 2.
$( \mathbf{ii})$ Find the probability that the spinner lands on a prime number
$( \textbf{iii})$ Find the probability that the spinner lands on the number 7.
(b) A bag contains 3 red balls and 12 green balls
Li picks a ball at random.
Find the probability that it is a green ball.
Give your answer as a fraction in its simplest form
$(\mathbf{c})$ Li spins two fair 4-sided spinners, each numbered l to 4.
The two numbers are multiplied to give the score
Find the probability that the score is
(i) an even number
(ii) an integer
(iii) at least 10.
$( \mathbf{d} )$ A bag contains red discs and blue discs.
The probability that a disc picked at random is red is $\frac{1}{5}.$
Li picks a disc at random, notes its colour and then replaces it in the bag
She then picks another disc at random.
(i) Complete the tree diagram.
$( \textbf{ii) }$ Work out the probability that both of the discs she picks are blue.
▶️Answer/Explanation
(a)(i): Arrow at $\frac{1}{2}$
(a)(ii): $\frac{1}{2}$
(a)(iii): $0$
(b): $\frac{4}{5}$
(c)(i): $\frac{3}{4}$
(c)(ii): $1$
(c)(iii): $\frac{3}{16}$
(d)(i): 
(d)(ii): $\frac{16}{25}$
Question8
(a) Fine area of this trapezium
(b)
The area of this triangle is $15.3$ cm$^{2}$.
Find the value of $b.$
$( \mathbf{c} )$ A circle has a circumference of 58.6cm.
Find the radius of this circle.
(d)
The diagram shows a rectangle with two semicircles removed.
Calculate the shaded area.
▶️Answer/Explanation
(a): $56.2$ or $56.16$
(b): $6.8$
(c): $9.33$ or $9.325$ to $9.327$
(d): $223$ or $222.8$ to $222.91$
Question9
$( \mathbf{a} )$ Line$L$ has a gradient of 4 and passes through the point (0,3).
Write down the equation of line $L$ in the form $y=mx+c.$
$\begin{array}{ll}{\mathbf{(b)}}&{{\mathrm{Line~}G\text{ has the equation }y=2-6x.}}\\&{{\mathrm{Line~}G\text{ passes through the point}(a,5).}}\end{array}$
Find the value of $a.$
$( \mathbf{c} )$ $( \mathbf{i} )$ Complete the table of values for $y= x^2- 6.$
(ii) One the grid , draw the graph of $y=x^2-6$ for $-4\leqslant x\leqslant 4$
\((\mathbf{iii})\quad\text{Write down the equation of the line of symmetry of the graph.}\)
\((\mathbf{iv})\quad\text{Use your graph to solve the equation}\quad x^2-6=0\quad\mathrm{for~}x>0.\)
▶️Answer/Explanation
(a): $y = 4x + 3$
(b): $-\frac{1}{2}$
(c)(i): $3 \quad -6 \quad 3$
(c)(ii): Correct curve
(c)(iii): $x = 0$
(c)(iv): $2.3$ to $2.6$