Question1
Write the number two million two thousand and two in figures
▶️Answer/Explanation
$2 \, 002 \, 002$
Question2
Put one pair of brackets into this calculation to make it correct
$$\begin{matrix}5&-&4&\times&3&-&9&-&2&=&0\end{matrix}$$
▶️Answer/Explanation
$5 – (4 \times 3 – 9) – 2$
Question3
Simplify.$7x-8y-x-y$
▶️Answer/Explanation
$6x – 9y \text{ or } 3(2x – 3y)$ (final answer)
Question4
The base of a cuboid measures $10$ cm by $7$ cm.
The volume of the cuboid is $280$ cm$^{3}.$
Calculate the height of the cuboid
▶️Answer/Explanation
$4$
Question5
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
$0.85 \, \text{oe}$
Question6
Factorise completely.$4x^2y-5xy^2$
▶️Answer/Explanation
$xy(4x – 5y)$ (final answer)
Question7
The scale of a map is $1:40000$.
On the map the distance between two villages is $37$cm. Calculate the actual distance between the two villages. Give your answer in kilometres.
▶️Answer/Explanation
$14.8$
Question8
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
$\frac{6}{14} \text{ and } \frac{1}{14} \, \text{oe}$\\ $\frac{5}{14} \, \text{cao}$
Question9
The diagram shows a right-angled triangle.
Calculate $AB.$
▶️Answer/Explanation
$6.39 \text{ or } 6.389\ldots$
Question10
Find the gradient of the line joining the points (-2,7) and (3,1).
▶️Answer/Explanation
$-\frac{6}{5} \, \text{oe}$
Question11
Solve the simultaneous equations
$$\begin{array}{c}5t-2w=19\\3t+2w=5\end{array}$$
▶️Answer/Explanation
$[t = 3] \quad [w = -2]$
Question12
Simplify.
$( \mathbf{a} )$ $\frac {32g^{16}}{16g^{8}}$
$( \mathbf{b} )$ $( 625k^8) ^{\frac 14}$
▶️Answer/Explanation
[(a)] $2g^8$ (final answer)
[(b)] $125k^6$ (final answer)
Question13
$(\mathbf{a})$
Shade the region $A\cup B^{\prime}.$
$(\mathbf{b})$
Use set notation to describe the shaded region
▶️Answer/Explanation
(a)
(b) $R \cap (P \cup Q’) \, \text{or} \, R \cap P’ \cap Q’ \, \text{oe}$
Question14
$P,Q,R$ and $T$ are points on the circle.
$AB$ is a tangent to the circle at $T.$
Angle $ATP=50^\circ$, angle $PTR=48^\circ$ and $PQ=QR$
(a) Find angle $PRT.$
$( \mathbf{b} )$ Find angle $QPR.$
▶️Answer/Explanation
(a) $50$
(b) $24$
Question15
The time taken for each of 200 students to complete a calculation is measured. The cumulative frequency diagram shows the results.
Use the diagram to find an estimate for
$(\mathbf{a})$ the interquartile range
$(\mathbf{b})$ the number of students taking more than 40 seconds to complete the calculation.
▶️Answer/Explanation
(a) $11$
(b) $6$
Question16
$$A=\pi r^2+\pi dh$$
Rearrange the formula to make $h$ the subject
▶️Answer/Explanation
$\frac{A – \pi r^2}{\pi d} \, \text{oe final answer}$
Question17
Work out, giving each answer in standard form.
$( \mathbf{a} )$ $\left ( 2. 1\times 10^{101}\right ) \times \left ( 8\times 10^{101}\right )$
$( \mathbf{b} )$ $\left ( 2. 1\times 10^{101}\right ) + \left ( 2. 1\times 10^{100}\right )$
▶️Answer/Explanation
(a) $1.68 \times 10^{203}$
(b) $2.31 \times 10^{101}$
Question18
\(\begin{aligned}&\text{The diagram shows two sides, }VA\mathrm{~and~}VB,\text{ of a regular polygon.}\\&AVX\text{ is a straight line.}\\&\mathrm{Angle~}BVX=y^{\circ}\text{ and angle }AVB=11.5y^{\circ}.\\&\text{Find the number of sides of this polygon.}\end{aligned}\)
▶️Answer/Explanation
$25$
Question19
\(\text{(a) Describe fully the single transformation that maps triangle T onto triangle W.}\)
\(\text{(b) Draw the enlargement of triangle T with scale factor -2 and centre of enlargement (-1,1).}\)
▶️Answer/Explanation
(a) $\text{Rotation: 90° clockwise oe}$
$(0, -2)$
(b) $\text{Triangle at: } (-5, -1), (-5, -7), (-7, -7)$
Question20
$\mathrm{f}(x)=3^x+2$
$( \mathbf{a} )$ Find $x$ when f$(x)=245.$
$( \mathbf{b} )$ Find $x$ when $f^-1(x)=7.$
▶️Answer/Explanation
(a) $5$
(b) $2189$
Question21
Write the recurring decimal $0.41$ as a fraction in its simplest form
You must show all your working.
▶️Answer/Explanation
$41.11\ldots – 41.11\ldots \, \text{oe} \\
\frac{37}{90} \, \text{cao}$
Question22
Solve the equation $tan~x+ \sqrt 3= 0$ for $0^{\circ}\leq x\leq360^{\circ}.$
▶️Answer/Explanation
$120, \, 300
$
Question23
Simplify.
$$\frac{2}{y+1}-\frac{3}{y}$$
Give your answer as a single fraction in its simplest form.
▶️Answer/Explanation
$\frac{-y – 3}{y(y + 1)} \, \text{or} \, \frac{-y – 3}{y^2 + y} \, \text{or} \, \frac{-y + 3}{y(y + 1)} \\
\text{or} \, \frac{-y + 3}{y^2 + y} \, \text{(final answer)}$
Question24
The diagram shows a triangular prism with cross-section triangle $BCV.$
Angle $BCV=90^{\circ},BC=5$cm,$CV=4$cm and $AB=15$cm.
Calculate the angle between $AV$ and the base $ABCD.$
▶️Answer/Explanation
$14.2 \, \text{or} \, 14.19 \, \text{to} \, 14.20
$
Question25
\(\begin{array}{cc}\mathrm{Simplify.}&\\&\underline{pt-p-t+1}\\&1-t^2\end{array}\)
▶️Answer/Explanation
$\frac{1 – p}{1 + t} \, \text{(final answer)}
$
Question26
In the diagram, $O$ is the origin.
$\overrightarrow{OP}=\mathbf{p}$ and $\overrightarrow {OQ}=\mathbf{q}.$
$R$ is the point of intersection of $PQ$ and $OS$,with $PR: RQ= 1: 2$ and $OR=RS.$
Find the position vector of $S$ in terms of p and q
Give your answer in its simplest form.
▶️Answer/Explanation
$\frac{4}{3}p + \frac{2}{3}q \, \text{oe}$