Home / 0580_s23_qp_22

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

$\frac{1}{3}$

Scroll to Top