4MA1 Mathematics A: Oct/Nov 2020 Paper 1HHigher Tier Paper 1

The numbers from 1 to 14 are shown in the Venn diagram.

(a)List the members of the set A ∩ B

[1]

(b)List the members of the set Bʹ

[1]

A number is picked at random from the numbers in the Venn diagram.

(c)Find the probability that this number is in set A but is not in set B.

[2]

Toy cars are made in a factory. The toy cars are made for 15 hours each day. 5 toy cars are made every 12 seconds.

For the toy cars made each day, the probability of a toy car being faulty is 0.002

Work out an estimate of the number of faulty toy cars that are made each day.

[4]

On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3

[3]

Here is a list of six numbers written in order of size.

a median of 9 a mean of 11

Find the value of x and the value of y.

x =

y = [4]

(a)Write 5.7 × 10^–3 as an ordinary number.

[1]

(b)Write 800 000 in standard form.

[1]

(c)Work out 3 × 106 × 10₋₂

[2]

A rocket travelled 100 km at an average speed of 28 440 km/h.

Work out how long it took the rocket to travel the 100 km. Give your answer in seconds, correct to the nearest second.

_seconds[3]

(a)Solve 5(4 – x) = 7 – 3x Show clear algebraic working.

x = [3]

(b)Factorise fully 16m³ g³+ 24m² g⁵

[2]

(c)(i)Factorise y²– 2y – 48

[2]

(ii)Hence, solve y²– 2y – 48 = 0

[1]

Here is a 10-sided polygon.

Work out the value of x.

x = [4]

In a sale, normal prices are reduced by 20%

A bag costs 1080 rupees in the sale.

Work out the normal price of the bag.

_rupees[3]

A = 2 × 3⁴³ B = 16 × 3³⁷

(a)Find the highest common factor (HCF) of A and B.

[1]

(b)Express the number A × B as a product of powers of its prime factors. Give your answer in its simplest form.

[2]

The diagram shows trapezium ABCD in which BC and AD are parallel.

The trapezium has exactly one line of symmetry.

BC = 8.4 cm AD = 17.6 cm

The trapezium has area 179.4 cm²

Work out the size of angle ABC. Give your answer correct to 1 decimal place.

[6]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [4]

Jan invests $8000 in a savings account. The account pays compound interest at a rate of x % per year.

At the end of 6 years, there is a total of $8877.62 in the account.

Work out the value of x. Give your answer correct to 2 decimal places.

x = [3]

F is inversely proportional to the square of v.

Given that F = 6.5 when v = 4

find a formula for F in terms of v.

[3]

Harry has two fair 5-sided spinners.

Harry is going to spin each spinner once.

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that at least one of the spinners will land on green.

[3]

L, M, N and P are points on a circle, centre O

Angle MNP = 58°

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

(ii)Give a reason for your answer.

[2]

(b)Find the size of the reflex angle MOP

[2]

A metal block has a mass of 5 kg, correct to the nearest 50 grams. The block has a volume of (1.84 × 10^–3) m³, correct to 3 significant figures.

Work out the upper bound for the density of the block. Give your answer in kg/m³ correct to 1 decimal place. Show your working clearly.

_kg/m³[4]

The table gives information about the heights, in centimetres, of some plants.

(a)On the grid, draw a histogram for this information.

[3]

(b)Work out an estimate for the number of these plants with a height greater than 40 cm.

[2]

Without using a calculator, rationalise the denominator of 63 −

Simplify your answer. You must show each stage of your working.

[3]

R and S are two similar solid shapes.

Shape R has surface area 108 cm² and volume 135 cm³ Shape S has surface area 300 cm²

Work out the volume of shape S.

_cm³[3]

Express

as a single fraction in its simplest form.

[5]

ABCD is a rhombus.

The diagonals, AC and BD, intersect at the point M. The coordinates of M are (6, −11)

The points A and C both lie on the line with equation 2y + 7x = 20

Find the exact coordinates of the point where the line through B and D intersects the y-axis.

( , )[4]

Curve C has equation y = px³− mx where p and m are positive integers.

Find the range of values of x, in terms of p and m, for which the gradient of C is negative.

[4]

Here are the first five terms of an arithmetic sequence.

Work out the sum of all the terms from the 50th term to the 100th term inclusive.

[4]

The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by the single transformation T.

(a)Describe fully the transformation T.

[1]

The diagram shows the graph of y = f(x)

(b)On the grid, draw the graph of y = 2f(x – 1)[2]