4MA1 Mathematics A: May/June 2019 Paper 2HHigher Tier Paper 2

The table shows information about the heights, in cm, of 48 sunflowers in a garden centre.

Height of sunflower (h cm) Frequency

Work out an estimate for the mean height of the sunflowers.

cm[4]

Use ruler and compasses to construct the perpendicular bisector of the line DE. You must show all your construction lines.

[2]

E ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 3, 5, 7} B = {4, 6, 8, 10}

(a)Explain why A ˆ
B = ‡

[1]

x E and x  A ‰ B

(b)Write down the two possible values of x.

_, [1]

Set C is such that

A ‰ B ‰ C =E A ˆ
C = {2} B ˆ
C

(c)List all the members of set C.

[2]

A cylinder has diameter 14 cm and height 20 cm.

Work out the volume of the cylinder. Give your answer correct to 3 significant figures.

cm³[2]

Josh buys and sells books for a living.

He buys 120 books for £4 each.

He sells 12 of the books for £5 each.

He sells 40% of the books for £7 each. He sells the rest of the books for £8 each.

(a)Calculate Josh’s percentage profit.

%[5]

One book that Josh owns had a value of £15 on the 1st May 2019 The value of this book had increased by 20% in the last year.

(b)Find the value of the book on the 1st May 2018

£ [3]

ABC and DEF are similar triangles.

(a)Work out the length of DF.

cm[2]

(b)Work out the length of BC.

cm[2]

30 students in a class sat a Mathematics test. The mean mark in the test for the 30 students was 26.8

13 of the 30 students in the class are boys. The mean mark in the test for the boys was 25

Find the mean mark in the test for the girls. Give your answer correct to 3 significant figures.

[3]

Change a speed of x kilometres per hour into a speed in metres per second. Simplify your answer.

m/s[3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

The straight line LKDVJUDGLHQWDQGSDVVHVWKURXJKWKHSRLQWZLWKFRRUGLQDWHV í

(a)Write down an equation for L.

[2]

(b)

The region R, shown shaded in the diagram, is bounded by four straight lines.

Write down the inequalities that define R.

[2]

The table gives the average crowd attendance per match for each of five football clubs for one season.

Football club Average crowd attendance

(a)Find the difference between the average crowd attendance for Barcelona and the average crowd attendance for Monaco. Give your answer in standard form.

[2]

Antonio says,

(b)Is Antonio correct? You must give a reason for your answer.

[2]

During last season the cost of a ticket to watch Seapron United increased by 15% and then decreased by 8%

(c)Work out the overall percentage change in the cost of a ticket to watch Seapron United during last season.

%[2]

ABCD is a trapezium.

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

cm[4]

The table gives information about the times taken, in minutes, for 80 taxi journeys.

Time taken (t minutes) Frequency

(a)Complete the cumulative frequency table.

Time taken (t minutes) Cumulative frequency

[1]

(b)On the grid opposite, draw a cumulative frequency graph for your table.

[2]

(c)Use your graph to find an estimate for the median.

minutes[1]

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

minutes[2]

Here are two vectors.

Find the magnitude of AC .

[3]

Make x the subject of the formula y =

4 + 8[4]

Show that can be written in the form a + b 2, where a and b are integers.

Show each stage of your working clearly and give the value of a and the value of b.[3]

y is directly proportional to the cube of x y = 20 h when x = h (h ≠ 0)

(a)Find a formula for y in terms of x and h

y = [3]

(b)Find x in terms of h when y = 67.5 h Give your answer in its simplest form.

x = [2]

The diagram shows a solid cuboid.

The total surface area of the cuboid is A cm²

Find the maximum value of A.

[5]

ABCD is a quadrilateral.

The area of triangle ACD is 250 cm²

Calculate the area of the quadrilateral ABCD. Show your working clearly. Give your answer correct to 3 significant figures.

cm²[6]

The equation of the line L is y x The equation of the curve C is x²íxy + 2y²= 0

L and C intersect at two points.

Find the coordinates of these two points. Show clear algebraic working.

( , ) and ( , )[5]

The diagram shows cuboid ABCDEFGH.

Calculate the size of the angle between AF and the plane ABCD. Give your answer correct to one decimal place.

[3]

Simplify fully₂

[3]

Boris has a bag that only contains red sweets and green sweets.

Boris takes at random 2 sweets from the bag.

The probability that Boris takes exactly 1 red sweet from the bag is 1235

Originally there were 3 red sweets in the bag.

Work out how many green sweets there were originally in the bag. Show your working clearly.

[5]

The function f is such that f (x) = 3x – 2

(a)Find f (5)

[1]

The function g is such that g(x) = 2x²– 20x + 9 where x . 5

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

g^–1(x) = [4]