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Question1

CDE is a straight line.
Find angle ADE.

▶️Answer/Explanation

$51$

Question2

A train journey starts at 21 43.
It takes 8 hours and 32 minutes.
Find the time the journey finishes.

▶️Answer/Explanation

$06\ 15$ or $6:15$ am

Question3

The diagram shows a straight line intersecting two parallel lines.
Find the value of a and the value of b, giving a geometrical reason for each answer.
a = ………………. because 
b = ………………. because 

▶️Answer/Explanation

 $58$, vertically opposite. $122$, interior.

Question4

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the
value of $\frac{6.7\times 2.1}{1.8-5.9}$
You must show all your working.

▶️Answer/Explanation

 $\frac{7 \times 2}{20 – 6}$. $1$

Question5

 Eric has four colours of paint.
The table shows the probability that he uses each colour.

Find the value of x.

▶️Answer/Explanation

$0.22$

Question6

Calculate the volume of a sphere with diameter 4.8cm.
[The volume, V, of a sphere with radius r is $V= \frac{4}{3}\pi r^3 $]

▶️Answer/Explanation

$57.9$ or $57.90$ to $57.91…$

Question7

The scale of a map is 1 : 125000.
On a map, the length of an island is 9.4cm.
Calculate the actual length of the island, giving your answer in kilometres.

▶️Answer/Explanation

$11.75$

Question8

(a) The nth term of a sequence is $10-n^2$ .

Write down the first three terms of this sequence.

(b) These are the first four terms of another sequence.
7              10            13         16
Find an expression for the nth term of this sequence.

▶️Answer/Explanation

(a): $961$

(b): $3n + 4$

Question9

Triangle ABC is similar to triangle DEF.
Calculate the value of h.

▶️Answer/Explanation

$6.3$

Question10

Without using a calculator, work out $2\frac{1}{7}\div \frac{5}{9}$

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

▶️Answer/Explanation

 $\frac{15}{7} \times \frac{9}{5}$ or $\frac{135}{63} \div \frac{35}{63}$ (with common denominator)

$3\frac{6}{7}$

Question11

Describe the single transformation that maps
(a) triangle A onto triangle B
(b) triangle A onto triangle C.

▶️Answer/Explanation

(a): Enlargement, scale factor 2, centre $(0, 7)$

(b): Rotation, centre $(3, 1)$, $90^\circ$ clockwise

Question12

AO, OB and OC are all radii of the circle.
AB = BC.
Therefore triangle AOB is congruent to triangle COB.
Draw a ring around the correct criterion for this statement.
SAS                 RHS              SSS         ASA

P, Q, R and S are points on the circle and TQU is a tangent to the circle at Q.
PR and SQ intersect at the centre of the circle, O, and PQ is parallel to SR.
Angle RQU = 42°.
Calculate

(i) angle QSR

(ii) angle PQS

(iii) angle POS.

▶️Answer/Explanation

(a): SSS (Side-Side-Side)

(b)(i): $42$

(b)(ii): $42$

(b)(iii): $84$

Question13

Anya invests $\$6000$ in an account that pays compound interest at a rate of r% per year.
At the end of 8 years, the account has earned $\$621.7$ in interest.
Calculate the value of r.

▶️Answer/Explanation

$1.24[0…]$

Question14

y is directly proportional to the square of (x + 3).
When x = 2, y = 5.
Find y when x = 1.

▶️Answer/Explanation

$3.2$

Question15

A bag contains 5 green buttons, 2 blue buttons and 6 white buttons.
Maya takes two buttons at random from the bag, without replacement.
Calculate the probability that one button is green and the other button is not green.

▶️Answer/Explanation

$\frac{20}{39}$

Question16

(a) Find the magnitude of the vector $\binom{-4}{5}$

The diagram shows a triangle OAC.
A is the midpoint of the straight line OB.
$\vec{OA} = x$ and $\vec{OC} = y$.
Find $\vec{CB}$ in terms of x and y.

▶️Answer/Explanation

(a): $6.40$ or $6.403…$

(b): $2x – y$

Question17

Simplify $(81.x^{12})^\frac{3}{4}$

▶️Answer/Explanation

$27x^9$

Question18

The diagram shows the position of three towns, U, V and W.
U is due west of V and angle UVW = 125°.
Calculate the bearing of U from W.

▶️Answer/Explanation

 $236$

Question19

(a) On the diagram, sketch the graph of y = cos x for $0° \leq x \leq 360° $.

(b) Solve the equation $5cos x+3 = 0$ for $0° \leq x \leq 360° $.

▶️Answer/Explanation

(a): Correct sketch

(b): $126.9$ or $126.86$ to $126.87$. $233.1$ or $233.13$ to $233.14$

Question20

The table shows some values for $y= 3x^2-2x-1$

(a) Complete the table. 
(b) On the grid, draw the graph of $y=3x^2-2x-1$ for $-1\leq x\leq 1.5$

 

(c) By drawing a suitable straight line, solve the equation $3x^2-4x-2=0$ for $-1\leq x\leq 1.5$

▶️Answer/Explanation

(a): $0.75$ and $-1.25$

(b): Correct curve

(c): ruled line $y = 2x + 1$. $-0.35$ to $-0.45$

Question21

A curve has equation $y=x^3-12x$.

(a) Find the gradient of the curve at the point (1,−11).

(b) Find the coordinates of the turning points of the curve.

▶️Answer/Explanation

(a): $-9$

(b): $(-2, 16)$, $(2, -16)$

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