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

(a)

Write down the inequality shown on the number line.

[1]

(b)Solve the inequality 4y - y + 8

[2]

Show that 5 23 í 34 = 2 1112[3]

(a)Complete the table of values for y = 1 + 5xíx²

[2]

(b)On the grid, draw the graph of y = 1 + 5xíx² for values of x

[2]

ABC and DEF are similar triangles.

(a)Work out the length of DE.

_cm[2]

The area of triangle DEF is 525 cm²

(b)Find the area of triangle DEF in m²

_m²[2]

Factorise x²íx

[2]

There are some ice lollies in a freezer.

The flavour of each ice lolly is banana or strawberry or mint or chocolate.

Julius takes at random an ice lolly from the freezer.

The table shows the probabilities that the flavour of the ice lolly that Julius takes is banana or strawberry or chocolate.

Work out the probability that the flavour of the ice lolly that Julius takes is either strawberry or mint.

[3]

A football team played 55 games. Each game was won, drawn or lost.

number of games won : number of games drawn : number of games lost = 6 : 3 : 2

Work out how many more games the team won than the team lost.

[3]

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

[2]

(b)Find the lowest common multiple (LCM) of A and B.

[2]

(a)Write 840 000 in standard form.

[1]

(b)Work out (6 × 10⁷) ÷ (8 × 10^í) Give your answer in standard form.

[2]

Henri buys a yacht for 150 000 euros.

The yacht depreciates in value by 18% each year.

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

_euros[3]

Line L is drawn on the grid.

Find an equation for L.

[3]

Calculate the length of AB. Show your working clearly. Give your answer correct to 3 significant figures.

_m[5]

Sandeep recorded the length of time, in minutes, that each of 100 adults went for a walk one Saturday afternoon.

The cumulative frequency table gives information about these times.

(a)On the grid, draw a cumulative frequency graph for the information in the table.

[2]

(b)Use your graph to find an estimate for the median length of time that these adults went for a walk.

_minutes[2]

One of the 100 adults is chosen at random.

(c)Use your graph to find an estimate for the probability that this adult went for a walk for more than 72 minutes.

[3]

(a)Simplify fully (x¹² y⁸)^3/4

[2]

Given that 3ⁿ = 39_y

(b)find an expression for n in terms of x and y.

n = [2]

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

AOC is a diameter of the circle.

Angle AOD = 98°

Work out the size of angle DBC. Give a reason for each stage in your working.

[4]

The following table gives values of x and y where y is inversely proportional to the square of x.

(a)Find a formula for y in terms of x.

[3]

Given that x  0

(b)find the value of x when y = 144

[2]

The table gives information about the first six terms of a sequence of numbers.

Prove algebraically that the sum of any two consecutive terms of this sequence is always a square number.[4]

The functions f and g are defined as

(a)State which value of x must be excluded from any domain of the function f.

[1]

(b)Find fg(x). Simplify your answer.

fg(x) = [2]

(c)Express the inverse function f^í in the form f^í(x) = …

f^í(x) = [3]

Part of the curve with equation y = h(x) is shown on the grid.

(d)Find an estimate for the gradient of the curve at the point where x í Show your working clearly.

[3]

The diagram shows a sector OAPB of a circle, centre O.

AB is a chord of the circle. Angle AOB = 80°

The area of sector OAPB is 252 ʌ cm²

Work out the perimeter of the shaded segment. Give your answer correct to 3 significant figures.

_cm[6]

6a

a = 3.46 correct to 3 significant figures. b = 6.3 correct to 1 decimal place.

Work out the upper bound for the value of x. Give your answer as a decimal correct to 3 significant figures. Show your working clearly.

[3]

The diagram shows two similar bottles, A and B.

Bottle A has surface area 240 cm² Bottle B has surface area 540 cm² and volume 2025 cm³

Work out the volume of bottle A.

_cm³[3]

Write 5 + 12xíx² in the form a + b(x + c)² where a, b and c are integers.

[4]

The diagram shows a solid pyramid ABCDE with a horizontal base.

The base, BCDE, of the pyramid is a square of side 10 cm.

The vertex A of the pyramid is vertically above the centre O of the base so that AB = AC = AD = AE

The total surface area of the pyramid is 360 cm²

Work out the size of the angle between AC and the base BCDE. Give your answer correct to 3 significant figures.

[6]

A box contains marbles.

4 of the marbles are red. The rest of the marbles are yellow.

Antonia takes at random a marble from the box and does not replace it. Sergio then takes at random a marble from the box.

The probability that Antonia and Sergio both take a yellow marble is 0.7

Work out how many marbles were originally in the box. Show your working clearly.

[5]