4MA1 Mathematics A: May/June 2018 Paper 1HHigher Tier Paper 1

The table shows information about the weights, in kg, of 40 parcels.

(a)Write down the modal class.

[1]

(b)Work out an estimate for the mean weight of the parcels.

_kg[4]

There are some people in a cinema.

35 of the people in the cinema are children.

For the children in the cinema,

number of girls : number of boys = 2 : 7

There are 170 girls in the cinema.

Work out the number of adults in the cinema.

[5]

(a)Simplify y⁵ × y⁹

[1]

(b)Simplify (2m³)⁴

[2]

(c)Solve 5(x + 3) = 3x – 4 Show clear algebraic working.

x = [3]

(d)(i)Factorise x²+ 2x – 24

[2]

(ii)Hence, solve x²+ 2x – 24 = 0

[1]

Here is a Venn diagram.

E

(a)Write down the numbers that are in the set

(i)A

(ii)B ∪ C

[2]

Brian writes down the statement A ∩ C = Ø

(b)Is Brian’s statement correct? You must give a reason for your answer.

[1]

One of the numbers in the Venn diagram is picked at random.

(c)Find the probability that this number is in set Cƍ

[2]

(a)Write 8 × 10⁴ as an ordinary number.

[1]

(b)Work out (3.5 × 10⁵) ÷ (7 × 10⁸) Give your answer in standard form.

[2]

M, N and P are points on a circle, centre O. MON is a diameter of the circle.

MP = 3.5 cm PN = 9.7 cm

Angle MPN = 90q

Work out the circumference of the circle. Give your answer correct to 3 significant figures.

_cm[4]

Chao bought a boat for HK$160 000 The value of the boat depreciates by 4% each year.

(a)Work out the value of the boat at the end of 3 years. Give your answer correct to the nearest HK$.

HK$ [3]

Jalina gets a salary increase of 5% Her salary after the increase is HK$252 000

(b)Work out Jalina’s salary before the increase.

HK$ [3]

A = 3⁵ × 5 × 7³ B = 2³ × 3 × 7⁴

(a)(i)Find the Highest Common Factor (HCF) of A and B.

(ii)Find the Lowest Common Multiple (LCM) of A and B.

[2]

A = 3⁵ × 5 × 7³ B = 2³ × 3 × 7⁴ C = 2^p × 5^q × 7^U

Given that the HCF of B and C is 2³ × 7 the LCM of A and C is 2⁴ × 3⁵ × 5² × 7³

(b)find the value of p, the value of q and the value of U.

p =

q =

U = [2]

The diagram shows a right-angled triangle.

Five of these triangles are put together to make a shape.

Calculate the perimeter of the shape. Give your answer correct to 3 significant figures.

_cm[5]

The cumulative frequency graph shows information about the length, in minutes, of each of 80 films.

80

70

60

50

(a)Use the graph to find an estimate for the interquartile range.

_minutes[2]

Clare says,

“More than 35% of these films are over 120 minutes long.”

(b)Is Clare correct? Give a reason for your answer.

[3]

(a)Expand and simplify (2x – 1)(x + 3)(x – 5)

[3]

(b)Solve 3x²+ 6x – 5 = 0 Show your working clearly. Give your solutions correct to 3 significant figures.

[3]

The diagram shows two straight lines drawn on a grid.

(a)Write down the solution of the simultaneous equations

x =

y = [1]

(b)Show, by shading on the grid, the region defined by all five of the inequalities

Label the region R.[3]

L, M and N are points on a circle, centre O. QMT is the tangent to the circle at M.

(a)(i)Find the size of angle NOM.

(ii)Give a reason for your answer.

[2]

(b)(i)Find the size of angle NMQ.

(ii)Give a reason for your answer.

[2]

The function f is such that

(a)Find f (–7)

[1]

(b)Express the inverse function f^–1 in the form f^–1(x) = ...

f ^–1(x) = [2]

The function g is such that

(c)Find fg (3)

[2]

(d)Which values of x cannot be included in any domain of g?

[2]

⎛²⁰ ⎞_1/−/4

(a)Simplify fully ⎜₈ ⎟ ⎝ y ⎠

[2]

(b)Express − 16x + 10 as a single fraction in its simplest form.

[3]

A frustum is made by removing a small cone from a large cone. The cones are mathematically similar.

The large cone has base radius U cm and height h cm.

Given that

find an expression, in terms of h, for the height of the frustum.

_cm[4]

The diagram shows parallelogram ABCD.

AB = ⎛ 2⎞⎝ 7⎠ AC = ⎛10⎞⎝11⎠

The point B has coordinates (5, 8)

(a)Work out the coordinates of the point C.

( , )[3]

The point E has coordinates (63, 211)

(b)Use a vector method to prove that ABE is a straight line.[2]

y

O x

The diagram shows the curve with equation y = f (x) The coordinates of the minimum point of the curve are (–2, –1)

(a)Write down the coordinates of the minimum point of the curve with equation

(i)y = f (x – 5)

( , )

(ii)y = 12 f (x)

( , )[2]

The graph of y = a sin(x – b)q + c for –90 - x -
450 is drawn on the grid below.

(b)Find the value of a, the value of b and the value of c.

a =

b =

c = [3]

Jack plays a game with two fair spinners, A and B.

Spinner A can land on the number 2 or 3 or 5 or 7 Spinner B can land on the number 2 or 3 or 4 or 5 or 6

Jack spins both spinners. He wins the game if one spinner lands on an odd number and the other spinner lands on an even number.

Jack plays the game twice. Work out the probability that Jack wins the game both times.

[4]

ABC is an isosceles triangle such that

AB = AC A has coordinates (4, 37) B and C lie on the line with equation 3y = 2x + 12

Find an equation of the line of symmetry of triangle ABC. Give your answer in the form px + qy = U where p, q and U are integers. Show clear algebraic working.

[5]