4MA1 Mathematics A: May/June 2023 Paper 2HHigher Tier Paper 2

Show that 4 23  115  3 89[3]

A biased spinner can land on green or on yellow or on brown or on pink.

The table gives the probabilities that, when the spinner is spun, it will land on green or on yellow or on brown.

Timucin spins the spinner 200 times.

Work out an estimate for the number of times the spinner lands on pink.

[3]

ABCD is a trapezium.

BC is parallel to AD

Find the size of the largest angle inside the trapezium.

[4]

(a)Complete the table of values for y = x²– x – 4

[2]

(b)On the grid below, draw the graph of y = x²– x – 4 for values of x from –3 to 3

[2]

Nancy has some coins with a total value of 85 pence. She has only 2 pence coins and 5 pence coins. The ratio

Nancy has more 5 pence coins than 2 pence coins.

How many more?

[4]

(a)Write 76 000 000 in standard form.

[1]

(b)Write 5.4 × 10 ^–4 as an ordinary number.

[1]

A and C are points on a circle, centre O DA is the tangent to the circle at A and DC is the tangent to the circle at C

Angle ADC = 48°

Work out the size of reflex angle AOC

[3]

Charlotte buys a painting for $680 The value of the painting increases by 4% each year.

Work out the value of the painting at the end of 3 years. Give your answer correct to the nearest $

$ [3]

Change a speed of 27 kilometres per hour to a speed in metres per second.

_m / s[3]

Team A and Team B take part in a quiz league.

After 11 rounds, Team A has a mean score per round of 17 After 9 rounds, Team B has a mean score per round of 18

Both teams take part in a further round. After this round, both teams have a mean score per round of 18.5

In the further round, Team A scored more points than Team B.

How many more?

[4]

Here is a 9-sided regular polygon ABCDEFGHJ, with centre O

ODK and FEK are straight lines.

Work out the value of x

x = [3]

The diagram shows right-angled triangle ABD

AB = 14 cm AD = 8 cm

C is the point on BD such that angle BAC = 38°

Work out the length of CD Give your answer correct to 3 significant figures.

_cm[4]

Narin has two fair 6-sided dice.

Dice A has 2 red faces and 4 yellow faces. Dice B has 1 red face and 5 yellow faces.

Narin is going to throw each dice once.

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that both dice land on yellow.

[2]

P, Q, R and S are points on a circle, centre O ROP is a diameter of the circle. Angle PRQ = 22°

(a)(i)Find the size of angle RQP

[1]

(ii)Give a reason for your answer.

[1]

(b)(i)Find the size of angle PSQ

[1]

(ii)Give a reason for your answer.

[1]

(a)Simplify fully 32a^{15 3/5}

[2]

(b)Express  10x  in the form pxⁿ where p and n are integers.

[2]

(c)Solve 1  2 y3  45  2 y  12

Show clear algebraic working.

y = [3]

Q is directly proportional to t The graph shows the relationship between Q and t for 0 < t < 8

(a)Find a formula for Q in terms of t

[3]

Q is increased by 20%

(b)Find the percentage increase in t

%[2]

(a)Expand and simplify (x + 6)(3x – 2)(x + 6)

[3]

(b)Make e the subject of w 

[4]

Here are 6 graphs.

Complete the table below with the letter of the graph that could represent each given equation.

Write your answers on the dotted lines.

x

[3]

Express 3x²– 6x + 5 in the form a(x – b)²+ c

[3]

There are 12 counters in a bag.

3 of the counters are red 9 of the counters are green

Ameya, Jack and Ella each take at random one counter from the bag.

Work out the probability that at least one red counter is still in the bag.

[3]

Solve the simultaneous equations

x = 3y – 1

Show clear algebraic working.

[5]

The diagram shows a triangle ABC and a flagpole BF

A, B and C are points on horizontal ground.

BF is vertical.

D is the point on AC such that angle BDC = 90°

Work out the size of the angle of elevation of the point F from the point D Give your answer correct to one decimal place.

[5]

The diagram shows a cuboid with a square cross section.

The volume of the cuboid is (13 + 6 5 ) cm³

Without using a calculator, find the value of x Give your answer in the form a + b where a and b are integers. Show your working clearly.

x = [4]

ABCD is a kite with AB = AD and CB = CD

A is the point with coordinates (–2, 10)

B is the point with coordinates   275 , 4

C is the point with coordinates (4, –5)

Work out the coordinates of D

( , )[6]

A solid sphere has a radius of 2.8 centimetres, correct to 1 decimal place. The sphere has a mass of M π grams, where M = 260 correct to 2 significant figures.

Work out the upper bound for the density of the sphere. Give your answer in g / cm³ correct to 2 decimal places. Show your working clearly.

_g / cm³[4]