Question1
The diagram shows two sides of a parallelogram ABCD.
Find the coordinates of point D.
▶️Answer/Explanation
$(-3,7)$
Question2
Geetha has a box of toys.
She picks a toy at random from the box.
The probability that she picks a wooden toy is $0.6$ .
(a) Work out the probability that she does not pick a wooden toy.
(b) The box contains three types of toys, wooden, plastic or metal.
Complete the table.
▶️Answer/Explanation
(a) $0.4$
(b)
Question3
The table shows some information about two sequences.
(a) Complete the table.
(b) Find the smallest positive number in sequence B.
▶️Answer/Explanation
(a)
(b) $24$
Question4
Find the greatest odd number that is a factor of $140$ and a factor of $210$.
▶️Answer/Explanation
$35$
Question5
Calculate.
$(\mathbf{a})\sqrt[3]{343}-\sqrt{40.96}$
$( \mathbf{b} )$ $( 192+ 4\times 16) ^{1. 25}$
▶️Answer/Explanation
(a) $0.6$
(b) $1024$
Question6
The diagram shows 5 kites that are congruent to kite $ABCD$
Each kite is joined to the next kite along one edge.
Angle $DAB=40^{\circ}$ and $DCE$ is a straight line.
Find the value of $x.$
▶️Answer/Explanation
$145$
Question7
The diagram shows a shape made from a triangle $JKL$ and a semicircle with diameter $JL$
$JKL$ is an isosceles right-angled triangle with $\tilde{J}K=JL=12.8$cm
(a) Calculate the area of this shape.
(b) Calculate the perimeter of this shape.
▶️Answer/Explanation
(a) 146
(b) 51
Question8
These are the first five terms of a sequence
$11 \quad \quad 18 \quad \quad 25 \quad \quad 32 \quad \quad 39$
Find an expression for the $n$th term of the sequence.
▶️Answer/Explanation
$7n+4$
Question9
The value of a car is \( \$8000\).
Each year the value of the car decreases exponentially by $25\%$
Calculate the value of this car after $3$ years
▶️Answer/Explanation
$3375$
Question10
Amir invests \(\$1500\) in an account.
The account pays compound interest at a rate of $r\%$ per year At the end of 8 years the value of his investment is \( \$1656.73\) . Find the value of $r.$
▶️Answer/Explanation
$1.25$
Question11
Find the inequalities that define the unshaded region, R.
▶️Answer/Explanation
\(\begin{array}{l}{y<x}\\{x<6}\\{1\leqslant y\leqslant5\mathrm{oe}}\end{array}\)
Question12
Solve the simultaneous equations. You must show all your working.
$$\frac{3x}{2}+5y=5\\4x-3y=46$$
▶️Answer/Explanation
Correctly equating one set of coefficients
Correct method to eliminate one variable
$x = 10, y = –2$
Question13
The diagram shows a cyclic quadrilateral.
Find the value of p.
▶️Answer/Explanation
$62$
Question14
The diagram shows a circle with radius 9cm.
Calculate the area of the shaded major sector.
▶️Answer/Explanation
$221$
Question15
Write $0.146$ as a fraction in its simplest form.
You must show all your working.
▶️Answer/Explanation
$\frac{29}{198}$
Question16
(a) In the Venn diagram, shade the region $M^{\prime}\cap N^{\prime}.$
(b) Find n$(B\cap(A^{\prime}\cup C)).$
▶️Answer/Explanation
(a)
(b) $17$
Question17
Calculate the area of triangle ABC.
▶️Answer/Explanation
$19.5$
Question18
The diagram shows the graph of $y=x^3+4x^2-2$ for $-3\leqslant x\leqslant1.5.$
By drawing a suitable straight line, solve the equation $x^3+4x^2-2=2x$ for $-3\leqslant x\leqslant1.5.$
▶️Answer/Explanation
(a)
$y=2x$ ruled
$x=-0.5$ to $-0.55$
$x=0.85$ to $0.9$
Question19
Factorise completely.
$( \mathbf{a} )$ $12m^2- 75t^2$
$( \mathbf{b} )$ $xy+ 15+ 3y+ 5x$
▶️Answer/Explanation
(a) $3(2m+5t)(2m-5t)$ final answer (b) $(x+3)(y+5)$ final answer
Question20
Solve the equation $8\sin x+ 6= 1$ for $0^{\circ}\leqslant x\leqslant360^{\circ}.$
▶️Answer/Explanation
$218.7,321.3$
Question21
$HD=4$cm$,EH=6.5$cm and $EF=9.1$ cm.
Calculate the angle between $CE$ and the base $CDHG.$
▶️Answer/Explanation
$33.2$ or $33.18…$
Question22
Bag $A$ and bag $B$ each contain red counters and blue counters only
Stephan picks a counter at random from bag $A$ and Jen picks a counter at random from bag $B.$
The probability that Stephan picks a red counter is $0.4$.
The probability that Stephan and Jen both pick a red counter is $0.25$.
Find the probability that Stephan and Jen both pick a blue counter.
▶️Answer/Explanation
$0.225$