4MA1 Mathematics A: Oct/Nov 2020 Paper 2HRHigher Tier Paper 2

The probability that a spinner will land on blue is 0.4

Rayyan is going to spin the spinner 280 times. Work out an estimate for the number of times the spinner will land on blue.

[2]

Write 880 as a product of powers of its prime factors. Show your working clearly.

[3]

(a)Write 2.46 × 10⁶ as an ordinary number.

[1]

(b)Write 0.000 74 in standard form.

[1]

(c)Work out (5.6 × 10⁶) + (2.3 × 10⁵)

[2]

Alexa has five cards. Each card has a number on it.

The table gives information about the numbers on the five cards.

Using the information in the table, complete each card by writing its number on it.[3]

The length of a book is 33.8 cm, correct to one decimal place.

(a)Write down the lower bound of the length of the book.

_cm[1]

(b)Write down the upper bound of the length of the book.

_cm[1]

Nav has worked out 68 .3 × 42 .80. 021 on his calculator.

His answer is 139 201.9048

Without using a calculator and using suitable approximations, check that his answer is sensible. Show your working clearly.[2]

Markus makes a steel framework. The framework is in the shape of the right‑angled triangle ABC shown in the diagram.

The steel that Markus uses costs $22 per metre. The steel can only be bought in a length that is a whole number of metres.

Work out the total cost of the steel that Markus buys in order to make the framework.

$ [4]

Alison buys 2 boxes of strawberries, box A and box B.

Box A contains 15 strawberries. The strawberries in box A have a mean weight of 24 grams.

Box B contains 25 strawberries. The strawberries in box B have a mean weight of 18 grams.

Alison puts all 40 strawberries into a bowl. Work out the mean weight of the 40 strawberries.

_grams[3]

(a)Factorise x²– x – 42

[2]

(b)Solve the inequality 3x + 15 < 8x + 3

Show clear algebraic working.

[3]

Given that 150^x = 1

(a)write down the value of x.

x = [1]

Given that 3^–8÷ 3^–6= 3ⁿ

(b)find the value of n.

n = [1]

Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.

[3]

Find the gradient of the straight line with equation 5x + 2y = 7

[2]

The diagram shows four congruent right‑angled triangles ABJ, BCI, CDH and DEG. The diagram also shows the straight line ABCDEF.

AJ = 15 cm Angle BAJ = 35°

AF = 80 cm

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

_cm[5]

Sandeep sat 11 tests in January 2020 Each test was marked out of 60

Here are his test results.

(a)Find the interquartile range of these test results. Show your working clearly.

[3]

Sandeep also sat some tests in May 2020 Each test was marked out of 60

The median of the May 2020 test results is 42 The interquartile range of the May 2020 test results is 12

(b)In which month, January or May, were Sandeep’s test results more consistent? Give a reason for your answer.

[1]

Platinum nuggets are in the shape of a solid cylinder.

The radius of each cylinder is 2.5 cm. The length of each cylinder is 15 cm.

The density of platinum is 21.5 g/cm³

The greatest mass that Jacques can carry is 30 kg.

Can Jacques carry 5 platinum nuggets at the same time? You must show all your working.[5]

A, B, C, D and E are points on a circle.

Angle EAC = 40°

(a)(i)Write down the size of angle EBC.

[1]

(ii)Give a reason for your answer.

[1]

(b)Find the size of angle EDC.

[1]

Given that n > 0

make n the subject of the formula y = + dn₂

[4]

(a)Complete the table of values for y = 12 x³– 2x + 3

[2]

(b)On the grid, draw the graph of y = 12 x³– 2x + 3 for –3  x  3

[2]

(c)By drawing a suitable straight line on the grid, find an estimate for the solution of

the equation 12 x³– x + 4 = 0

x = [2]

A, B, C and D are points on a circle with centre O and radius 12 cm.

The area of the sector OADC of the circle is 100 cm²

Work out the size of angle ABC. Give your answer correct to 3 significant figures.

[4]

T is inversely proportional to m²

T = 30 when m = 0.5

(a)Find a formula for T in terms of m.

[3]

(b)Work out the value of T when m = 0.1

[1]

The histogram gives information about the times, in minutes, some customers had to wait to be served in a restaurant.

14 customers had to wait less than 10 minutes to be served.

Work out the number of customers who had to wait less than 60 minutes to be served.

[3]

The curve with equation x²– x + y²= 10 and the straight line with equation x – y = –4 intersect at the points A and B.

Work out the exact length of AB.

Show your working clearly and give your answer in the form a2 where a is an integer.

[6]

P and Q are two points.

The coordinates of P are (–1, 6)

The coordinates of Q are (5, –4)

Find an equation of the perpendicular bisector of PQ. Give your answer in the form ax + by + c = 0 where a, b and c are integers.

[6]

(a)Write 7 + 12x – 3x² in the form a + b(x + c)² where a, b and c are integers.

[4]

The curve C has equation y = 7 + 12x – 3x² The point A is the turning point on C.

(b)Using your answer to part (a), write down the coordinates of A.

( , )[1]

OAN, OMB, APB and MPN are straight lines.

OA : AN = 1 : 4

OM : MB = 1 : 1 → → OA = 2a OB = 2b

By using a vector method, find the ratio AP : PB Give your answer in its simplest form.

[5]

A, B, D and E are points on a circle. ABC and EDC are straight lines.

(2 + 5 ) cm

BC = (2 + 5 ) cm

ED = (4 + 5 ) cm

DC = 2 5 cm

Show that the length of AB is ( p 5 + q) cm, where p and q are integers whose values are to be found. Show your working clearly.[5]