4MA1 Mathematics A: May/June 2018 Paper 2FFoundation Tier Paper 2

(a)Write 0.63 as a fraction.

[1]

(b)Write 46 821 correct to the nearest 100

[1]

(c)Write 73.654 correct to 1 decimal place.

[1]

(d)Write 0.09 as a percentage.

%[1]

Daniel has five bags of coloured sweets. He picks at random a sweet from each bag. The table shows the probability that the sweet he picks from each bag is red.

(a)From which bag is Daniel least likely to pick a red sweet?

[1]

(b)Which bag contains only red sweets?

[1]

(c)From which bag is Daniel equally likely to pick a red sweet as a sweet of another colour?

[1]

Joseph buys some heating oil. He puts it in his oil tank.

The scales show the numbers of litres of oil in the tank immediately before and immediately after Joseph puts the oil in the tank.

The oil Joseph buys costs 0.40 euros per litre.

Work out the total cost of the oil that Joseph buys.

_euros[3]

The diagram shows points A, B and C on a square grid.

(a)Write down the coordinates of C.

( , )[1]

(b)Measure the length of BC. Give your answer in centimetres.

_cm[1]

(c)On the grid, mark with a cross (X) the point D so that ABCD is a parallelogram. Label this point D.[1]

(a)Write down a multiple of 8 that is between 20 and 50

[1]

There is only one prime number that is an even number.

(b)Write down this number.

[1]

Shreya says that 57 is a prime number.

(c)Is Shreya correct? Give a reason for your answer.

[1]

Here is a sequence of patterns made from dots.

(a)Draw Pattern number 4 in the space above.[1]

(b)Complete the table.

[1]

(c)Work out the number of dots in Pattern number 13

[2]

(d)Find an expression, in terms of n, for the number of dots in Pattern number n.

[1]

There are fewer than 90 dots in Pattern number k.

(e)What is the largest possible value of k?

[2]

(a)Write 7 × 7 × 7 × 7 × 7 as a power of 7

[1]

(b)Show that 64 is both a square number and a cube number.[2]

(c)Find the value of 11³

[1]

(d)Find the value of 98.01

[1]

(a)Find the value of 25 – 4 g when g = –3

[2]

(b)Expand and simplify x(2x + 1) + 3(x – 2) + 7

[3]

R and S are points on a circle with centre O.

(a)On the diagram above, shade a segment of the circle.[1]

(b)Write down the mathematical name of the straight line RS.

[1]

In the diagram below, P and Q are points on a circle with centre O.

QT is a tangent to the circle. Angle OPQ = 18q

(c)Work out the size of angle PQT. Give a reason for each stage of your working.

[3]

Last Thursday, 135 students each bought one item of fruit. The table shows information about the 135 items of fruit they bought.

One of the 135 students is chosen at random.

(a)Find the probability that this student bought an apple or a banana.

[2]

A pie chart is drawn for the information in the table.

(b)Work out the size of the angle in the pie chart for oranges.

[2]

(a)Work out the value of 10 .45.1 − 2.7 + 6.8 − 3.29.5

Give your answer as a decimal. Write down all the figures on your calculator display.

[2]

(b)Give your answer to part (a) correct to 3 significant figures.

[1]

The diagram shows a quadrilateral ABCD on a centimetre grid.

(a)Work out the area of triangle ABC. You must include the units with your answer.

[3]

(b)Give a reason why angle ACD is equal to angle CAB.

[1]

(c)Write down an equation for the straight line that passes through D and C.

[1]

Tenzin walks in the mountains. She has a rule to estimate the temperature at different heights on a mountain.

Temperature decreases by 2 qC for every increase of 300 metres in height.

The temperature at a height of 800 metres on a mountain is 6 qC.

(a)Use Tenzin’s rule to work out an estimate of the temperature at a height of 2000 metres on the mountain.

qC[3]

Tenzin also has a rule to estimate the time it will take her to complete a walk in the mountains.

She uses an average speed of 5 km / h for the distance she will walk and then adds on 1 minute for every increase of 10 metres in height.

Tenzin plans to walk 12 km in the mountains with an increase of 800 metres in height.

(b)Use Tenzin’s rule to work out an estimate for the time it will take her to complete this walk. Give your answer in hours and minutes.

_{hours minutes}[3]

Javier has two sets of cards. Each set contains 4 cards, one marked A, one marked B, one marked C and one marked D.

Javier is going to take at random one card from each set. The table shows all possible pairs of cards that Javier could take.

(a)Find the probability that Javier will take at least one card marked C.

[2]

Javier is going to take at random one card from each set, note the letter on each card and replace the cards.

He is going to do this a total of 80 times.

(b)Work out an estimate for the number of times that Javier will take at least one card marked C.

[2]

BCDE is a rectangle. ABE is an isosceles triangle.

AB = AE Angle BAE = 80q

Work out the size of angle x.

[3]

Work out the difference between the largest share and the smallest share when 3450 yen is divided in the ratios 2 : 6 : 7

_yen[3]

Gopal is paid 20 000 rupees each month. Jamuna is paid 19 200 rupees each month.

Gopal and Jamuna are both given an increase in their monthly pay. After the increase, they are both paid the same amount each month.

Gopal was given an increase of 8%

Work out the percentage increase that Jamuna was given.

%[4]

(a)Make a the subject of the formula M = ac – bd

[2]

(b)Solve the inequality 5x – 4  39

[2]

(c)Factorise fully 18e² f³– 12e³ f

[2]

The diagram shows two cylinders, A and B.

Cylinder A has height 1.6 m and radius 0.56 m.

(a)Work out the curved surface area of cylinder A. Give your answer in m² correct to 3 significant figures.

_m²[2]

Cylinder B is mathematically similar to cylinder A. The height of cylinder B is 0.6 m.

(b)Work out the radius of cylinder B.

_m[2]

Show that 3 47 − 158 = 1 5356[3]

Work out the value of x. Give your answer correct to 3 significant figures.

x = [3]

The students in Class A and in Class B take the same examination.

There are 28 students in Class A and 32 students in Class B. The mean score for all the students in both classes is 72.6 The mean score for the students in Class A is 75

(a)Work out the mean score for the students in Class B.

[4]

The lowest score in Class A is 39 The range of scores for Class A is 57 The lowest score in Class B is 33 The range of scores for Class B is 60

(b)Find the range of scores for all the students in both classes.

[3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y =

[3]

(a)Find the value of n.

n = [2]

(13^–6)⁴ × 13⁵= 13^k

(b)Find the value of k.

k = [2]