Question1
Write the number two million two thousand and two in figures.
▶️Answer/Explanation
$2002002$
Question2
Put one pair of brackets into this calculation to make it correct.
$$\begin{matrix}5&+&4&\times&3&+&9&=&53\end{matrix}$$
▶️Answer/Explanation
$5+4\times(3+9)=53$
Question3
Simplify.
$$7x-8y-x-y$$
▶️Answer/Explanation
$6x-9y$ or $3(2x-3y)$ final answer
Question4
(a) Write $164703$ correct to the nearest thousand.
(b) Write $16.983$ correct to l decimal place.
(c) Write $0.037665$ correct to 2 significant figures.
▶️Answer/Explanation
(a) $165 000$ cao
(b) $17.0$ cao
(c) $0.038$ cao
Question5
(a)On the diagram, draw any lines of symmetry.
(b) Write down the order of rotational symmetry of this shape.
▶️Answer/Explanation
(a) Correct line of symmetry
(b) $3$
Question6
Write these numbers in order, starting with the smallest.
$$0.45\quad \quad \quad 42\%\quad \quad \quad \frac4{11}\quad \quad \quad \frac25$$
▶️Answer/Explanation
$\frac 4{11}$ $\frac 25$ $42\% 0. 45$
Question7
The base of a cuboid measures l0cm by $7$cm.
The volume of the cuboid is 280 cm$^{3}$
Calculate the height of the cuboid.
▶️Answer/Explanation
$4$
Question8
In a city, the probability that it will rain today is $0.15$.
Find the probability that it will not rain today in this city
▶️Answer/Explanation
$0.85$
Question9
One day the temperature in Tokyo is $-5^\circ$C and the temperature in Manila is $18^\circ$C .
(a) Work out the difference between these two temperatures
(b) The temperature in Tokyo rises by $4^{\circ}$C.
Find the new temperature in Tokyo.
▶️Answer/Explanation
(a) $23$
(b) $-1$
Question10
(a) These are the first four terms of a sequence.
$3$ $10$ $17$ $24$
(i) Write down the next term.
(ii) Write down the term to term rule for continuing the sequence.
(b) These are the first four terms of another sequence.
$16$ $14$ $11$ $7$
Write down the next two terms of this sequence.
▶️Answer/Explanation
(a)(i) $31$
(a)(ii) add $7$
(b) $2$ $-4$
Question11
The diagram shows an isosceles triangle.
Find the value of x.
▶️Answer/Explanation
$108$
Question12
The diagram shows a cuboid.
on the $1 \rm {cm}^3$ grid, complete a net of this cuboid.
One face has been drawn for you.
▶️Answer/Explanation
Fully correct net
Question13
Factorise completely.
$4x^2y-5xy^2$
▶️Answer/Explanation
$xy(4x – 5y)$ final answer
Question14
The scale of a map is $1:40 000$.
On the map the distance between two villages is 37cm. Calculate the actual distance between the two villages. Give your answer in kilometres.
▶️Answer/Explanation
$14.8$
Question15
Without using a calculator, work out $\frac{3}{7}-\frac{1}{14}.$
You must show all your working and give your answer as a fraction in its simplest form
▶️Answer/Explanation
$\frac{6}{14}$ and $\frac{1}{14}$
$\frac{5}{14}$ cao
Question16
The price of a game increases from \(\$48\) to \(\$56.40\) .
Calculate the percentage increase in the price.
▶️Answer/Explanation
$17.5$
Question17
The diagram shows a right-angled triangle.
Calculate $AB.$
▶️Answer/Explanation
$6.39$
Question18
The length, s metres, of a ship is 83 m, correct to the nearest metre.
Complete this statement about the value of s.
▶️Answer/Explanation
$82.5$
Question19
Solve the simultaneous equations.
$$\begin{array}{l}5t-2w=19\\3t+2w=5\end{array}$$
▶️Answer/Explanation
$[t = ] 3$
$[w = ] –2$
Question20
The diagram shows the positions of three towns $A,B$ and $C.$
Angle $ABC=103^{\circ}.$
The bearing of town $B$ from town $A$ is 48°.
Town $C$ is due east of town $A.$
Find the bearing of town $C$ from town $B.$
▶️Answer/Explanation
$125$
Question21
(a)
$\mathcal{E}= \{ 1, 4, 5, 8, 9, 12, 16, 64\}$
$C=\{$cube numbers$\}$
$S=\{$square numbers$\}$
(i) Complete the Venn diagram
(ii) Find n$(C\cup S).$
(b)
On this Venn diagram, shade the region $A\cap B.$
▶️Answer/Explanation
(a)(i)
(a) (ii) $6$
(b)
Question22
(a) Write these numbers in standard form.
(i) $0.007$
(ii) $700000000$
(b) Calculate $\frac {3200\times 5. 4\times 10^{- 3}}{4. 8\times 10^{- 4}}.$
Give your answer in standard form.
▶️Answer/Explanation
(a) (i) $7\times10^{-3}$
(a) (ii) $7\times10^8$
(b) $3.6\times10^4$
Question23
The diagram shows a sphcrical tank with radius 0.5 m and a cylindrical jug with diameter $24$cm and height $32$cm. The tank is full of water.
Calculate how many times the jug can be completely filled with water from the tank
[The volume, $V$, of a sphere with radius $r$ is $\frac43\pi r^3.]$
▶️Answer/Explanation
$36$