Question1
From the list of numbers, write down
(a) a cube number
(b) a prime number
▶️Answer/Explanation
(a): 27
(b): 29
Question2
$\textbf{v}= \begin{pmatrix} – 1\\ 3\end{pmatrix}$ $\textbf{y}= \begin{pmatrix} 2\\ 5\end{pmatrix}$
Find
$( a)$ $v- y$
$(b)2v.$
▶️Answer/Explanation
(a): $\begin{pmatrix} -3 \\ -2 \end{pmatrix}$
(b): $\begin{pmatrix} -2 \\ 6 \end{pmatrix}$
Question3
On the Venn diagram, shade the region $A \cap B$
▶️Answer/Explanation
Correct shading
Question4
$23, 17, 11, 5,………$
(a) Write down the next number in this sequence
(b) Find the nth term of this sequence
▶️Answer/Explanation
(a): $-1$
(b): $29 – 6n$
Question5
Factorise completely. $8g-2g^2$
▶️Answer/Explanation
$2g(4 – g)$
Question6
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 $\frac{4}{7} \div \frac{56}{7}$. $\frac{1}{14}$
Question7
\(\begin{array}{cc}(\mathbf{a})&15t+8=4-t\\\\(\mathbf{b})&\frac{25-2u}{3}=2\end{array}\)
▶️Answer/Explanation
(a): $-\frac{1}{4}$
(b): $9.5$
Question8
Calculate $0.3^2.$
Give your answer in standard form.
▶️Answer/Explanation
$9 \times 10^{-2}$
Question9
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. $x = 5$, $y = -2$
Question10
In the diagram, $AB$ and $CD$ are parallel The lines $CB$ and $AD$ intersect at $X.$ $AB=3.0$ cm, $AX=2.0$ cm, $BX=2.7$ cm and $CD=7.5$ cm
Find the length of $BC.$
▶️Answer/Explanation
$9.45$
Question11
Find the highest common factor (HCF) of 12x$^{12}$ and 16x$^{16}.$
▶️Answer/Explanation
$4x^{12}$
Question12
In a regular polygon, the interior angle and the exterior angle are in the ratio $\textbf{interior: exterior= 11: 1.}$
Find the number of sides of this regular polygon.
▶️Answer/Explanation
$24$
Question13
The diagram shows the speed–time graph for part of a car journey
Calculate the total distance travelled during the $10$ seconds
▶️Answer/Explanation
$90$
Question14
The diagram shows a sector of a circle with centre O and radius $9$cm
The length of the chord PQ is $6$ cm
Calculate the length of the arc PQ
▶️Answer/Explanation
$6.12$ or $6.116…$ to $6.118$
Question15
Simplify $(3125w^{3125})^{\frac{1}{5}}$
▶️Answer/Explanation
$5w^{625}$
Question16
$y$ is inversely proportional to $x^2.$
${\mathrm{When~}}x=3,y=2.$
Find $y$ when $x=2.$
▶️Answer/Explanation
$4.5$
Question17
$ABCD$ is a cyclic quadrilateral, $ABX$ is a straight line and $PQ$ is a tangent to the circle at $A.$
Angle $CBX=85^{\circ}$, angle $BAQ=55^{\circ}$ and angle $CAD=42^{\circ}.$
Find
$( \mathbf{a} )$ angle $CBD$
$( \mathbf{b} )$ angle $ACB$
$( \mathbf{c} )$ angle $ADC$
$( \mathbf{d} )$ angle $BCD$
$( \mathbf{e} )$ angle $PAD.$
▶️Answer/Explanation
(a): $42$
(b): $55$
(c): $85$
(d): $108$
(e): $53$
Question18
Two solids are mathematically similar and have volumes $81$ cm3 and $24$ cm3 The surface area of the smaller solid is $44$ cm2
Calculate the surface area of the larger solid
▶️Answer/Explanation
$99$
Question19
\(\text{Find the values of x when 6x}+y=10\quad\mathrm{and}\quad y=x^2-3x+10.\)
▶️Answer/Explanation
$0$ and $-3$
Question20
Find the $n$th term of each sequence
$(\mathbf{a})$ $-1,\quad 0,\quad7,\quad26,\quad63,\quad…$
$( \mathbf{b} )$ $24\quad , 12\quad, 6\quad, 3\quad, 1.5, \ldots$
▶️Answer/Explanation
(a): $(n-1)^3 – 1$
(b): $24 \times (\frac{1}{2})^{n-1}$
Question21
A car travels $14$km, correct to the nearest kilometre. This takes $12$ minutes, correct to the nearest minute. Calculate the lower bound of the speed of the car.
Give your answer in kilometres per minute.
▶️Answer/Explanation
$1.08$
Question22
The diagram shows a triangular prism $ABCDQP$ of length $7$cm.
The cross-section is triangle $PA\hat{B}$ with $PA=\tilde{4}$cm, $AB=5$ cm and angle $PAB=90^\circ$
Calculate the angle between the line $PC$ and the base $ABCD.$
▶️Answer/Explanation
$24.9$ or $24.93$ to $24.94$
Question23
Simplify.
$\frac{5x^2-19x+12}{x^2-9}$
▶️Answer/Explanation
$\frac{5x-4}{x+3}$
Question24
The probability that he hits the target for the first time on his $n$th attempt is $\frac{64}{2187}.$
The probability of Jamie hitting a target is $\frac{1}{3}.$
Find the value of $n.$
▶️Answer/Explanation
$7$
Question25
\(\mathrm{f}(x)=x^3+1\mathrm~{Find~f}^{-1}(x).\)
▶️Answer/Explanation
$\sqrt[3]{x-1}$ or $(x-1)^{\frac{1}{3}}$