Exam Structure Set A: Foundation Paper 1

Question 1 [1 marks]

Area, Volume and Measures

A cube has edge length 4 cm. Which of the following is the total surface area of the cube?

Question 2 [1 marks]

Pythagoras and Trigonometry

Write down the trigonometric ratio that links opposite and hypotenuse. Use the word "sine" in your answer.

Question 3 [2 marks]

Indices and Standard Form

Write each of these numbers as an ordinary number.

3.6 x 10^5

4.02 x 10^-3

Question 4 [2 marks]

Angles and Geometrical Reasoning

Lines l and m are parallel and are crossed by a straight transversal. Angle y is in the corresponding position to the 118 degree angle marked above line l.

Question 5 [2 marks]

Sequences

Here are the first four terms of a sequence. 2, 6, 10, 14

Write down the next two terms of the sequence.

Describe, in words, the term-to-term rule for the sequence.

Question 6 [3 marks]

Fractions, Decimals and Percentages

(Non-calculator)

Write 45% as a decimal.

Write 3/4 as a percentage.

Write 0.2 as a percentage.

Question 7 [1 marks]

Statistics and Probability

Using the diagram in Question 10, write down n(F).

Question 8 [1 marks]

Number and Calculation

Calculate 125 x 8.

Question 9 [1 marks]

Statistics and Probability

A school recorded the time, t minutes, spent on homework by 30 pupils in one evening. The table shows the results. Time, t (minutes): 0 < t <= 20, 20 < t <= 40, 40 < t <= 60, 60 < t <= 80, 80 < t <= 100 Frequency (f): 4, 9, 11, 4, 2 Total number of pupils = 30 Write down the modal class.

Question 10 [2 marks]

Linear Algebra

Solve 5 - 2x = 1 Show your working.

Question 11 [1 marks]

Number and Calculation

Work out 7 x 8.

Question 12 [1 marks]

Statistics and Probability

Priya says that 8 is a member of set A (using the sets in Question 1). Is she correct? Give a reason for your answer.

Question 13 [2 marks]

Number and Calculation

Work out the least common multiple of 14, 21 and 35.

Question 14 [2 marks]

Statistics and Probability

Grace kept a record of the number of books read last month by 20 pupils in her form. The table shows the results. Books read (x): 0, 1, 2, 3, 4 Frequency (f): 3, 7, 6, 3, 1 Total number of pupils = 20 Find the median number of books read.

Question 15 [1 marks]

Number and Calculation

Work out 8 x 6.

Question 16 [2 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (-1, 6) and (3, -2).

Question 17 [2 marks]

Indices and Standard Form

Simplify 20y^9 / 5y^3.

Question 18 [2 marks]

Graphs and Coordinates

Rearrange 2y = 8x - 6 into the form y = mx + c and state the gradient.

Question 19 [2 marks]

Number and Calculation

Show that 123456 is divisible by 3.

Question 20 [2 marks]

Ratio and Proportion

Given that a : b = 5 : 2 and a = 25, work out the value of b.

Question 21 [2 marks]

Area, Volume and Measures

Convert 4.5 km into metres.

Question 22 [2 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (2, 5) and (8, 1).

Question 23 [2 marks]

Linear Algebra

Expand and simplify (4x - 3)(2x + 5)

Question 24 [2 marks]

Quadratics

Solve x^2 + 9x = 0

Question 25 [2 marks]

Number and Calculation

Show that 108 = 2^2 x 3^3.

Question 26 [4 marks]

Ratio and Proportion

Priya mixes squash and water in the ratio 1:6 (squash : water). Let s be the amount of squash in litres and w the amount of water. Write w as a linear function of s in the form w = ks and give k.

Question 27 [3 marks]

Quadratics

A rectangular lawn has width x metres and length (x + 5) metres. The area of the lawn, A m^2, is given by A = x(x + 5).

Complete the table of values for A = x(x + 5), for 1 <= x <= 3. x : 1 , 2 , 3 A : _ , _ , _

Explain why, in this context, x cannot take a negative value.

Question 28 [3 marks]

Graphs and Coordinates

Priya walks from home to the bus stop, waits for the bus, then travels quickly by bus to college. Sketch a distance-time graph to show Priya's journey. Label your axes Time and Distance from home.

Question 29 [5 marks]

Linear Algebra

A triangle has angles of (2x + 10) degrees, (3x - 5) degrees and (x + 25) degrees.

Show that 6x + 30 = 180

Hence find the size of the smallest angle in the triangle.

Question 30 [3 marks]

Quadratics

For each equation, state whether its graph is u-shaped or n-shaped.

y = 4 - 7x^2

y = 6x^2 - x - 1

y = -x^2 + 3x - 2

Question 31 [6 marks]

Linear Algebra

The diagram shows a rectangular photo frame. The perimeter of the frame is 50 cm.

Show that 8x + 2 = 50

Solve the equation to find the value of x.

Work out the length and the width of the frame, and state whether the frame is in landscape or portrait orientation.

Question 32 [6 marks]

Sequences

Here are the first four terms of an arithmetic sequence. 15, 11.5, 8, 4.5

Find the common difference of the sequence.

Find an expression, in terms of n, for the nth term of the sequence.

Find the first term in the sequence that is negative.

Question 33 [7 marks]

Graphs and Coordinates

The time, t hours, taken to fill a water tank is inversely proportional to the number of pumps, n, used. When n = 4, t = 3.

Find a formula for t in terms of n.

Complete the table of values for t = 12/n. n : 1 , 2 , 3 , 4 , 6 t : _ , _ , _ , 3 , _

State one feature of the graph of t against n, for n > 0.