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

The table gives information about the weights, in kilograms, of five animals.

(a)Which animal has the least weight?

[1]

(b)Write down the value of the 1 in the number 3178

[1]

(c)Work out the difference between 2205 and 1013

[1]

The weight of a blue whale is 20 times the weight of the giraffe.

(d)Work out the weight of the blue whale. Give your answer in tonnes. 1 tonne = 1000 kg

_tonnes[2]

A field is in the shape of a rectangle.

The width of the field is 70 m. The length of the field is 100 m.

Fafa walks around the edge of the field 3 times.

Work out the total distance Fafa walks.

_m[3]

Here is a rectangle A made from centimetre squares.

(a)What fraction of rectangle A is shaded?

[1]

Rectangle B is made from centimetre squares.

(b)Shade 40% of rectangle B.[1]

(a)On the diagram, mark a right angle with the letter R.[1]

There is a quadrilateral in the diagram.

(b)Write down the mathematical name of this quadrilateral.

[1]

(c)Measure the size of angle x.

[1]

A, B and C are three points marked on a grid.

(a)On the grid, draw the line with equation x í Label the line L.[1]

M is the midpoint of AB.

(b)Find the coordinates of M.

( , )[2]

D is the point so that ABCD is a square.

(c)Find the coordinates of D.

( , )[2]

Here is a number machine.

(a)Work out the output when the input is 18

[1]

(b)Work out the input when the output is 20

[2]

Here is a different number machine.

For this number machine, when the input is 8 the output is 50

(c)Work out the value of x.

x = [2]

Here is a list of all the nut trees Caterina counted one day.

(a)Complete the frequency table for Caterina’s list.

[2]

(b)Draw a bar chart for the information in your table.[3]

(a)Simplify y u y u y

[1]

(b)Simplify 3c u 2d

[1]

(c)Simplify 2kík + 3k

[1]

The table shows the temperatures at midnight and at midday at five ski resorts.

(a)Which ski resort had the lowest temperature at midnight?

[1]

(b)Work out the increase in temperature from midnight to midday for Chamonix.

_°C[1]

Jan knows that the temperature falls by 1 °C for every 300 m increase in height above Asiago.

(c)What was the temperature at midnight at a height 1800 m above Asiago?

_°C[2]

There are 20 counters in bag X.

7 of the counters are green. 10 of the counters are red. The rest of the counters are blue.

Ruth takes at random a counter from bag X.

(a)Write down the probability that the counter is red.

[1]

(b)Work out the probability that the counter is blue.

[1]

Ruth puts the counter back into bag X.

Bag Y only contains green counters, red counters and blue counters.

In bag Y there are,

2 more green counters than in bag X 1 more red counter than in bag X 2 more blue counters than in bag X

Adam takes at random a counter from bag Y. Ruth takes at random a counter from bag X.

(c)Who has the greater probability of taking a green counter, Adam or Ruth? Show your working clearly.[3]

A sequence is formed by adding 1 to each square number. Here are the first five terms of the sequence.

(a)Find the 10th term of the sequence.

[1]

1025 is a term of this sequence.

(b)Which term?

[2]

ABC is a straight line. Work out the value of x.

x = [3]

Show that 78 í 16 = 1724[2]

y = cídx

c = 15 d = 8

(a)Work out the value of y.

y = [2]

t = 18 q = 6

(b)Work out the value of p.

p = [2]

There are 440 students at a school. The number of male students is 40 more than the number of female students.

65% of the male students like art. 85% of the female students like art.

Work out the total number of students at the school who like art.

[4]

Here is a hexagon ABCDEF.

CD is parallel to AF.

Work out the area of hexagon ABCDEF.

_cm²[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]

(c)Describe fully the single transformation that maps triangle P onto triangle Q.

[2]

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]

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

(a)Work out the value of E when n = 3

E = [1]

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

(b)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]