4MA1 Mathematics A: May/June 2019 Paper 1FFoundation Tier Paper 1

From the numbers in the box, write down

(a)an odd number

[1]

(b)a multiple of 12

[1]

(c)a square number

[1]

(d)a prime number

[1]

Complete the following statements by writing a number on each dotted line.

(a)A pentagon has sides.[1]

(b)The size of each angle in an equilateral triangle is [1]

(c)1 kilometre = metres.[1]

The table gives the surface areas, in square kilometres, of six lakes in Africa.

(a)Which of these lakes has the least surface area?

[1]

(b)Write the number 6405 in words.

[1]

(c)Write the number 68 879 correct to the nearest thousand.

[1]

Sammy says that the surface area of Lake Malawi is about 5 12 times the surface area of Lake Albert.

(d)Is Sammy correct? Give a reason for your answer.

[2]

The diagram shows a fair 6-sided spinner.

Rami is going to spin the spinner once.

(a)Circle the word in the box below that best describes the likelihood that the spinner will land on green.

[1]

(b)On the probability scale below, mark with a cross ( ×) the probability that the spinner will land on blue.

[1]

(c)On the probability scale below, mark with a cross ( ×) the probability that the spinner will land on yellow.

[1]

There are 12 481 people at a concert. 8906 of these people are adults. The rest of the people are children.

35 of the children are boys.

Work out the number of girls at the concert.

[4]

(a)Simplify 6e × 2f

[1]

(b)Simplify 5m + 7kím + k

[2]

(c)Solve 5y + 3 = 14

y = [2]

Here are the shoe sizes of 11 people.

(a)Write down the mode.

[1]

(b)Work out the range.

[2]

(c)Find the median.

[2]

Clark works in a shoe shop.

On Tuesday morning he sold some pairs of shoes. The mean price of the pairs of shoes was £34

On Tuesday afternoon he sold only two pairs of shoes. The prices of these pairs of shoes were £31 and £49

(d)Is the mean price of all the pairs of shoes Clark sold on Tuesday more or less than £34? You must give a reason for your answer.

[1]

The diagram shows two triangles, CDB and BDA.

Angle ABC = 90° Angle CDB = 116° Angle DAB = 55°

Work out the size of the angle marked x. Give a reason for each stage of your working.

[5]

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

[2]

(b)Show that 815 + 310 = 56[2]

(c)Show that 4 23 ÷ 1 19 = 4 15[3]

The pictogram gives information about the number of emails Sami sent on each of five days last week.

Work out the mean number of emails Sami sent on these 5 days.

[4]

(a)On the grid above, rotate the triangle 180° about (7, 6)[2]

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

[2]

(a)Use your calculator to work out the value of

Write down all the figures on your calculator display.

[2]

(b)Write your answer to part (a) correct to 1 significant figure.

[1]

Each exterior angle of a regular polygon is 24°

Work out the number of sides of the polygon.

[2]

(a)Find the highest common factor (HCF) of 40 and 64

[2]

A = 2ⁿ × 3 × 5^m

(b)Write 8A as a product of powers of its prime factors.

[2]

Jalina left her home at 10 00 to cycle to a park. On her way to the park, she stopped at a friend’s house and then continued her journey to the park. Here is the distance-time graph for her journey to the park.

(a)On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend’s house? Give a reason for your answer.

[1]

Jalina stayed at the park for 45 minutes. She then cycled, without stopping, at a constant speed of 16 km/h from the park back to her home.

(b)Show all this information on the distance-time graph.[2]

(c)Work out Jalina’s average cycling speed, in kilometres per hour, for the complete journey to the park and back. Do not include the times when she was not cycling in your calculation. Give your answer correct to 1 decimal place.

_km/h[3]

P = 2g + 3h

(a)Work out the value of P when g = 7 and h í

[2]

(b)Simplify e⁹÷ e⁵

[1]

[1]

(d)Expand and simplify (x + 9)(x – 2)

[2]

(e)Factorise fully 16c⁴ p²+ 20cp³

[2]

In a box,

number of red buttons : number of blue buttons = 5 : 3

number of blue buttons : number of green buttons = 1 : 2

There are 48 green buttons in the box.

Work out the number of red buttons in the box.

[4]

(a)Complete the table of values for y = x²íxí

[2]

(b)On the grid, draw the graph of y = x²íx x

[2]

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.

[4]

The diagram shows a solid cuboid made from wood.

The wood has density 0.7 g/cm³

Work out the mass of the cuboid.

_grams[3]

(a)Write 5.7 × 10⁶ as an ordinary number.

[1]

(b)Write 0.004 in standard form.

[1]

(c)Work out 2 × 106.4 × 10₋₂

[2]

On 1st January 2016 Li bought a boat for $170 000 The value of the boat depreciates by 8% per year.

Work out the value of the boat on 1st January 2019 Give your answer correct to the nearest dollar.

$ [3]

The diagram shows a shape made from a right-angled triangle and a semicircle.

AC is the diameter of the semicircle. BA = BC = 6 cm Angle ABC = 90°

Work out the area of the shape. Give your answer correct to 1 decimal place.

_cm²[5]