Question1
Find the temperature that is $8°C$ colder than $-5 °C$.
▶️Answer/Explanation
$-13$
Question2
There are two prime numbers in this list.
$27 \quad 47 \quad 57\quad 61\quad 75\quad 93$
Work out the sum of these two prime numbers.
▶️Answer/Explanation
$108$
Question3
On ten days, Stefan records the number of minutes he has to wait for a train.
$1 \quad3 \quad12\quad 5 \quad4 \quad23\quad 5\quad 24 \quad11 \quad8$
(a) Complete the stem-and-leaf diagram to show this information.
(b) Find the median.
▶️Answer/Explanation
4 1.4[0]
Question4
The distance from town $A$ to town $B$ on a map is $3.5$cm
The scale on the map is $1:250000.$
Find the actual distance, in kilometres, from town $A$ to town $B.$
▶️Answer/Explanation
$8.75$
Question5
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
$0.4$
Question6
$\mathcal{E}=\{x:1\leqslant x\leqslant20\}$
$E=\{$even numbers$\}$
$M=\{$multiples of 5$\}$
$(\mathbf{a})$ Find n$(M).$
$( \mathbf{b} )$ Find the elements in the set $E\cap M$
(c) $y\notin E.$
Write down a possible value of $y.$
▶️Answer/Explanation
(a): $4$
(b): $10, 20$
(c): An odd number or decimal in the range $1 < x < 20$
Question7
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). $\frac{6}{13}$
Question8
Solve.
$(\mathbf{a})$ $\frac{30}{x}=6$
$( \mathbf{b} )$ $11 x- 3\geqslant 2( 2x+ 9)$
▶️Answer/Explanation
(a): $5$
(b): $x > 3$
Question9
$F$ 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 $G$
$( \mathbf{d} )$ the magnitude of vector $\overline{GH}.$
▶️Answer/Explanation
(a): $\begin{pmatrix} 24 \\ -9 \end{pmatrix}$
(b): $\begin{pmatrix} -4 \\ 32 \end{pmatrix}$
(c): $(9, -7)$
(d): $37$
Question10
\(\begin{aligned}&\mathrm{(a)}\quad\text{Describe fully the single transformation that maps shape }A\text{ onto shape }B.\\&\mathrm{(b)}\quad\text{Rotate shape }A\text{ 90° clockwise about the point }(-1,2).\\&\mathrm{(c)}\quad\text{Enlarge shape }A\text{ by scale factor }-2,\mathrm{~centre~}(2,0).\end{aligned}\)
▶️Answer/Explanation
(a): Reflection, $y = 2$
(b): Shape at $(-2, -2)$, $(-6, -5)$, $(-6, -3)$, $(-4, -2)$
(c): Shape at $(0, -2)$, $(0, 2)$, $(-2, 6)$, $(-6, 6)$
Question11
The diagram shows a shape, $ABCD$, formed by the sectors of two circles with the same centre $O.$
Both sector angles are 140°, $OC=3.2$ cm and $CB=2.6$ cm .
The area of the shape is $k\pi\mathrm{cm}^2.$
Find the value of $k.$
▶️Answer/Explanation
$9.1$
Question12
One solution of the equation $ax^2+ b= 181$ is $x=8.$
$a$ and $b$ are both positive integers greater than 1.
$(\mathbf{a})$ Find the value of $b.$
$\mathbf{(b)}$ Write down the other solution of the equation $ax^2+b=181.$
▶️Answer/Explanation
(a): $53$
(b): $-8$
Question13
$A,B,C$ and $D$ are points on a circle.
$AB$ is parallel to $DC$ and angle $ACD=32^\circ.$
Chords $AC$ and $DB$ intersect at $E$
Find the value of $x.$
▶️Answer/Explanation
$116$
Question14
$$\mathrm{f}(x)=5x+2$$
Find $\mathrm f^{-1}(x).$
▶️Answer/Explanation
$\frac{x-2}{5}$
Question15
$C$ is the point $(5,-1)$ and $D$ is the point $(13,15)$
$(\mathbf{a})$ Find the midpoint of $CD.$
$(\mathbf{b})$ Find the gradient of $CD.$
$(\mathbf{c})$ Find the equation of the perpendicular bisector of $CD.$
Give your answer in the form $y=mx+c.$
▶️Answer/Explanation
(a): $(9, 7)$
(b): $2$
(c): $y = -\frac{1}{2}x + \frac{23}{2}$
Question16
Write $0.621$ as a fraction in its simplest form.
You must show all your working
▶️Answer/Explanation
$621.21… – 6.21…$ which simplifies to $\frac{41}{66}$
Question17
The diagram shows a triangle with an acute angle marked $x^{\circ}.$
The area of the triangle is $2143$ cm$^{2}.$
Work out the value of $x.$
▶️Answer/Explanation
$40.7$ or $40.73$ to $40.74$
Question18
Make x the subject of the formula.
$$c=\frac{3x}{2x-5}$$
▶️Answer/Explanation
$\frac{5c}{2c-3}$
Question19
$m$ is inversely proportional to the square of $(t+2).$
$m=0.64$ when $t=3$
Find $m$ when $t=8.$
▶️Answer/Explanation
$0.16$
Question20
In the Venn diagram, shade the region $A\cap B^{\prime}\cap C.$
▶️Answer/Explanation
Question21
Solve the equation $5 sinx=-3 $ for $0^{\circ}\leqslant x\leqslant360^{\circ}.$
▶️Answer/Explanation
$216.9$ or $216.86$ to $216.87$. $323.1$ or $323.13…$
Question22
Write as a single fraction in its simplest form.
$$\frac{5}{3x+2}+\frac{4}{2x-1}$$
▶️Answer/Explanation
$\frac{22x+3}{(3x+2)(2x-1)}$
Question23
\(\begin{aligned}&\mathrm{Bag~}A\text{ and bag }B\text{ each contain red sweets and yellow sweets.}\\&\text{Anna picks a sweet at random from bag }A.\\&\text{Ben picks a sweet at random from bag }B.\\&\text{The probability that Anna pricks a red sweet is }\frac{2}{5}.\\&\text{The probability Anna and Ben both pick a yellow sweet is }\frac{1}{10}.\\&\text{Find the probability that Anna and Ben both pick a red sweet.}\end{aligned}\)
▶️Answer/Explanation
$\frac{1}{3}$