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Question1

 Write the number twenty-five million in figures

▶️Answer/Explanation

$25000000$

Question2

$( \mathbf{a} )$ Write 0.7 as a fraction.

$( \mathbf{b} )$ Write $\frac{13}{20}$ as a percentage.

▶️Answer/Explanation

(a): $\frac{7}{10}$ or equivalent fraction

 (b): $65$

Question3

$-7\quad \quad -12\quad \quad-3\quad \quad-28\quad \quad-6\quad \quad15\quad \quad-4\quad \quad-8$

From the list of numbers, find

(a) all the numbers which are less than $-5$

(b) the product of the largest number and the smallest number.

▶️Answer/Explanation

(a): $-6, -7, -8$

(b): $-120$

Question4

An exam starts at 11 50 and lasts for 2$\frac{1}{4}$ hours.
Work out the time that the exam finishes.

▶️Answer/Explanation

$1405$ (representing 2:05 PM)

Question5

 Write $56.17345$ correct to $1$ decimal place.

▶️Answer/Explanation

$56.2$

Question6

Work out the number of seconds in $5$ hours.

▶️Answer/Explanation

$18000$

Question7

From the list of numbers, write down

(a) a cube number

$(\mathbf{b})$ a prime number.

▶️Answer/Explanation

(a): $27$

(b): $29$

Question8

$\textbf{v}= \begin{pmatrix} – 1\\ 3\end{pmatrix}$ $\textbf{y}= \begin{pmatrix} 2\\ 5\end{pmatrix}$

Find

$( a)$ $v- y$

$(b)2v.$

▶️Answer/Explanation

(a): $\begin{pmatrix} -3 \\ -2 \end{pmatrix}$

(b): $\begin{pmatrix} -2 \\ 6 \end{pmatrix}$

Question9

A suit costs $6500$ rupees.

Calculate the cost of the suit in dollars when the exchange rate is $1$ rupee $=\ $0.013$

▶️Answer/Explanation

 $84.50$

Question10

The diagram shows one face of a cuboid on a 1 cm2 grid.

The cuboid has a volume of $24$ cm3 .
Complete a net of this cuboid.

▶️Answer/Explanation

Fully correct net

Question11

The median of six numbers is $61$.
Five of the numbers are $24, 43, 58, 71$ and $85$.
Work out the sixth number.

▶️Answer/Explanation

$64$   

Question12

Work out the size of one interior angle of a regular $9$-sided polygon.

▶️Answer/Explanation

 $140$

Question13

On the Venn diagram, shade the region $A \cap B$

▶️Answer/Explanation

 

Question14

Factorise completely. $8g-2g^2$

▶️Answer/Explanation

$2g(4-g)$

Question15

The diagram shows a circle, centre O, with diameter AC.
A, B, C, D and E lie on the circumference of the circle.
(a) Find the value of x.
Give a reason for your answer.

(b) Find the value of y.
Give a reason for your answer.

▶️Answer/Explanation

(a): $25$. Angle in a semicircle $= 90^\circ$ 

(b): $46$. Base angles of an isosceles triangle are equal. 

Question16

Without using a calculator, work out $\frac{4}{7}\div 8$

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

▶️Answer/Explanation

$\frac{4}{7} \times \frac{1}{8}$ or $\frac{4}{7} \div \frac{56}{7}$. $\frac{1}{14}$

Question17

A school records how many calculators it sells each week for 40 weeks.
The results are shown in the table.

Work out the mean number of calculators the school sells each week.

▶️Answer/Explanation

$1.375$

Question18

The mass, $m$ kg, of a bag of sand is $12$kg, correct to the nearest kilogram.
Complete the statement about the value of $m$.

▶️Answer/Explanation

 $11.5$, $12.5$

Question19

Qianna invests $\$3000$ at a rate of $4\%$ per year compound interest.
Calculate the value of her investment at the end of $6$ years.

▶️Answer/Explanation

$3800$ or $3795$ or $3796$ or $3795.9…$

Question20

Solve.

$\frac{25-2u}{3}=2$

▶️Answer/Explanation

$9.5$

Question21

Calculate $0.3^2.$
Give your answer in standard form.

▶️Answer/Explanation

 $9 \times 10^{-2}$

Question22

The probability of passing a driving test is $0.36$
$600$ people take this driving test.
Work out the expected number of these people that will pass

▶️Answer/Explanation

$216$

Question23

Solve the simultaneous equations. You must show all your working

$$\begin{matrix}3x-2y=19\\x+y=3\end{matrix}$$

▶️Answer/Explanation

Correctly eliminating one variable. $x = 5$, $y = -2$

Question24

The diagram shows a right-angled triangle

Show that angle y is $31.9°$,correct to 1 decimal place

▶️Answer/Explanation

$\tan y = \frac{46}{74}$. $31.86$ to $31.87$

Question25

The diagram shows two right-angled triangles, ABC and ACD.
Work out the value of $x$.

▶️Answer/Explanation

 $60$

Question26

A circle has an area of $25\pi\mathrm{cm}^{2}.$

$\mathbf{(a)}$ Work out the circumference of the circle.
Give your answer in terms of $\pi.$

$\mathbf{(b)}$ Two of the circles are used as the ends of a cylinder, with height $h$ cm

The total surface area of the cylinder is $170\pi\mathrm{cm}^{2}.$

Work out the value of $h.$

▶️Answer/Explanation

(a): $10\pi$

(b): $12$

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