4MA1 Mathematics A: January 2019 Paper 1FRFoundation Tier Paper 1

The table gives information about the lengths of five canals.

(a)Which of these canals has the least length?[1]

The length of the Panama Canal is 77.1 km.

(b)Write 77.1 correct to the nearest 10[1]

The Kiel Canal was opened on June 20th 1895

(c)How many years old was the Kiel Canal on June 20th 2000?

[1]

(a)Write these fractions in order of size. Start with the smallest fraction.

[1]

(b)Write 14 as a decimal.[1]

(c)Write 15 as a percentage.

[1]

(d)Work out 1 − 58[1]

Here is a circle, centre O.

(a)Measure the radius, OP, of the circle. Give your answer in centimetres.

[1]

The point Q is 2 cm from O. The angle between OP and OQ is a right angle.

(b)Mark with a cross (×) a possible position of the point Q. Label the point Q.[2]

The bar chart gives information about the volume of fresh water made per day from sea water in each of four countries in 2015

(a)Write down the volume of fresh water made per day from sea water in Saudi Arabia in 2015

[1]

More fresh water was made per day from sea water in the UAE in 2015 than was made per day from sea water in Spain in 2015

(b)How much more?

[2]

1.7 million m³ of fresh water was made per day from sea water in Qatar in 2015

(c)Draw a bar on the bar chart to show this information.[1]

Here is a list of numbers.

(a)Which number in the list is a multiple of both 6 and 9?[1]

Two numbers in the list are factors of 90

(b)Which two numbers?

[2]

(c)Write down two numbers in the list that have a sum that is a prime number.

[1]

Juan and Gabriella and their two children are going on a train journey from Madrid.

The cost of an adult ticket for this train journey is 53.50 euros. The cost of a child ticket for this train journey is 60% of the cost of the adult ticket.

Juan buys 2 adult tickets and 2 child tickets. He pays with two 100 euro notes.

How much change should he get?

[4]

(a)Simplify 5x + 4y – x – y[2]

(b)Solve 2t + 3 = 12

[2]

Here is a sequence of patterns made from white counters and black counters.

(a)In the space below, complete Pattern number 4[1]

(b)Find the total number of counters in Pattern number 6[1]

(c)Work out the number of black counters in Pattern number 14[1]

(d)Work out the total number of counters in Pattern number 50[2]

There are 20 beads in a box.

7 of the beads are red. 11 of the beads are green. The rest of the beads are yellow.

Jan takes at random a bead from the box.

(a)Write down the probability that she takes a red bead.[1]

(b)Find the probability that she takes a red bead or a yellow bead.[2]

There are 26 counters in a bag.

5 of the counters are pink. 10 of the counters are blue. The rest of the counters are white.

Jan puts some more pink counters into the bag. She then takes some blue counters out of the bag. After she has done this there are still 26 counters in the bag.

Jan then takes at random a counter from the bag.

The probability that she takes a pink counter is 12

(c)What is the probability that she takes a blue counter?[3]

Here is a triangle S drawn on a grid of squares.

(a)On the grid, reflect triangle S in the line with equation x = 5 Label the new triangle T.[2]

(b)On the grid, reflect triangle T in the line with equation x = 2 Label the new triangle U.[1]

(c)Describe fully the single transformation that maps triangle S onto triangle U.[2]

Andros wants to make a playlist of four songs for a friend.

The total time taken by the four songs will be 20 minutes. The time taken by each of the first three songs is shown below.

First song 6 minutes 16 seconds

Second song 4 minutes 28 seconds

Third song 4 minutes 35 seconds

Work out the time taken by the fourth song. Give your answer in minutes and seconds.

[1]

(b)Work out 11⁴[1]

The fish tank is in the shape of a cuboid.

Jonah wants to keep 20 fish in the fish tank. He knows that he must have 9 litres of water for each fish in the fish tank.

What is the minimum depth of water in the fish tank that Jonah must have?

In the club, the ratio of the number of girls to the number of boys is 3 : 1

3 of the girls play a musical instrument. 5

45 of the boys play a musical instrument.

What fraction of the 60 children play a musical instrument?

S is the point on PR such that angle RSQ = 90° RQ = 14 cm RS = 10 cm SP = 5 cm

Work out the length of PQ.

a is the least number. 40 is the greatest number.

The range of the four numbers is 14 The median of the four numbers is 30

Work out the value of a and the value of b.

Work out the average speed of the train. Give your answer in kilometres per hour.

In the diagram, all the angles are in degrees.

RP = RQ

Find the value of y. Show clear algebraic working.

Show clear algebraic working.

(a)Write N as a number in standard form.[1]

(b)Write N as a product of powers of its prime factors. Show your working clearly.[3]

(c)Find the largest factor of N that is an odd number.[1]

The boys and the girls have some coins.

The mean number of coins that the boys have is 5.5 The girls have a total of 18 coins.

Work out the mean number of coins the 20 children have.