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

Here is a hexagon ABCDEF.

CD is parallel to AF.

Work out the area of hexagon ABCDEF.

_cm²[4]

The table gives information about the times, in hours, some students spent doing sport one week.

Time (T hours) Frequency

Calculate an estimate for the mean time these students spent doing sport. Give your answer in hours, correct to 1 decimal place.

_hours[4]

(a)Reflect triangle S in the line y = x Label the new triangle R.[2]

(b)Translate triangle S by the vector ⎛ −4⎞⎜

Label the new triangle T.[1]

Anna and Lionel share $675 in the ratio 4 : 5

Lionel gives 35 of his share of the money to his mother.

How much money does Lionel give to his mother?

$ [3]

E = n²+ n + 5

Ali thinks that the value of E will be a prime number for any whole number value of n.

Is Ali correct? You must give a reason for your answer.

[2]

ABC and DEF are parallel lines.

BG = BE Angle DEG = 38° Angle GEB = 65°

Find the size of angle ABG.

[3]

Here are the first four terms of an arithmetic sequence.

(a)Find an expression, in terms of n, for the nth term of this sequence.

[2]

(b)Write down an expression, in terms of n, for the (n + 1)th term of this sequence.

[1]

(a)Write 1 390 000 in standard form.

[1]

(b)Write 0.005 in standard form.

[1]

Here is an empty pool in the shape of a cuboid.

The width of the pool is 3 m. The length of the pool is 12 m. The top of the pool is 2.5 m above the base of the pool.

Jeb is going to put water in the pool. The level of the surface of the water will be 60 cm below the top of the pool.

Water flows into the pool at 400 litres per minute. 1 m³= 1000 litres

How long will it take to fill the pool to 60 cm below the top of the pool? Give your answer in hours and minutes.

_{hours minutes}[4]

Solve

Show clear algebraic working.

x =

y = [3]

Change a speed of 72 kilometres per hour to a speed in metres per second.

_{metrespersecond}[3]

A company makes cars.

In 2016, the company made 350 cars.

In the first 6 months of 2017, the company made 25 cars each month. In the last 6 months of 2017, the company made 45 cars each month.

(a)Work out the percentage increase in the number of cars the company made from 2016 to 2017

_%[4]

The company’s income in 2017 was $500 000 more than the company’s income in 2016

The company’s income in 2017 was 8% more than the company’s income in 2016

(b)Work out the company’s income in 2016

$ [3]

Each month Edna spends all her income on rent, on travel and on other living expenses.

She spends 13 of her income on rent.

She spends 15 of her income on travel.

She spends $420 of her income on other living expenses.

Work out her income each month.

$ [4]

(a)Simplify (2e² f³)³

[2]

(b)Expand and simplify (3xíy)(x + 3y)

[2]

(c)Find the value of k.

k = [2]

(d)Simplify 24_n − 1− 1

[2]

There are two bags of counters, bag X and bag Y.

There are 20 counters in bag X. 11 of the counters are blue and the rest are red.

There are 16 counters in bag Y. 9 of the counters are blue and the rest are red.

Arkady takes at random a counter from bag X and takes at random a counter from bag Y.

(a)Complete the probability tree diagram.

[3]

(b)Work out the probability that the two counters are both red.

[2]

(c)Work out the probability that the two counters are both red or are both blue.

[3]

The points B, C, Y and X lie on a circle.

AXY and ABC are straight lines.

AX = 12 cm XY = x cm AB = x cm BC = 4 cm

(a)Show that x²íx [3]

(b)Find the length of AC. Show your working clearly. Give your answer correct to 3 significant figures.

_cm[4]

The table gives information about the areas, in hectares, of some farms in Spain.

0  A - 20

20  A - 50

50  A - 100

100  A - 300

300  A - 350

On the grid, draw a histogram for this information.

4

3

[3]

Here is a quadrilateral PQRS.

Angle SRQ is acute.

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

[6]

The curve shown in the diagram has equation

The curve has a maximum point at A (a, b) The curve has a minimum point at B (c, d)

Using differentiation, find the value of bíd Show your working clearly.

[6]

Two functions, f and g are defined as

Given that h = fg

express the inverse function h^í in the form h^í: x 6 …

h^í: x 6 [4]

(a)Show that x(xí x + 1) = x³íx[1]

(b)Prove that the difference between a whole number and the cube of this number is always a multiple of 6[3]

A 3-D shape consists of a hollow sphere made of metal.

The diagram shows a cross section drawn through the centre, O, of the sphere.

The internal radius of the sphere is 1.2 m. The thickness of the metal is t cm.

The density of the metal is 2700 kg per m³

The mass of the 3-D shape is 1980 kg.

Work out the value of t. Give your answer correct to 2 significant figures.

t = [5]

Work out the sum of the multiples of 3 between 1 and 1000

[4]