Exam Structure Set B: Foundation Paper 1

Question 1 [1 marks]

Pythagoras and Trigonometry

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

Question 2 [3 marks]

Statistics and Probability

The probability scale below shows five points, labelled P, Q, R, S and T, marked at equal intervals between 0 and 1.

Sam rolls an ordinary fair dice numbered 1 to 6. Write down the letter of the point that best represents the probability that the score is less than 7.

A card is picked at random from a standard, well-shuffled pack of 52 playing cards. Write down the letter of the point that best represents the probability that the card is a spade.

A fair coin is flipped once. Write down the letter of the point that best represents the probability that it lands on tails.

Question 3 [3 marks]

Angles and Geometrical Reasoning

Column vectors are written in the form (x, y), where x is the top (horizontal) number and y is the bottom (vertical) number. u = (4, 1) and v = (-2, 5).

Work out u + v as a column vector.

Work out u - v as a column vector.

Work out 3v as a column vector.

Question 4 [3 marks]

Fractions, Decimals and Percentages

(Non-calculator) Work out 17.5% of 240.

Question 5 [1 marks]

Number and Calculation

Work out 402 / 6.

Question 6 [1 marks]

Ratio and Proportion

Write 3 to 8 as a ratio in its simplest form.

Question 7 [1 marks]

Quadratics

Write down the coordinates of the minimum point of the graph of y = (x - 2)^2 + 5.

Question 8 [1 marks]

Indices and Standard Form

Simplify (r^3)^4.

Question 9 [1 marks]

Statistics and Probability

A class of 24 students was asked whether they study French (F) or Spanish (S). The Venn diagram shows: French only = 6, both French and Spanish = 4, Spanish only = 9, and neither = 5. Write down the number of students who study both French and Spanish.

Question 10 [1 marks]

Angles and Geometrical Reasoning

A cuboid has length 6 cm, width 3 cm and height 2 cm. Write down the shape of the top elevation (the view from above).

Question 11 [1 marks]

Number and Calculation

Calculate 63 x 4.

Question 12 [1 marks]

Statistics and Probability

Using the same table as Questions 7 and 8: 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 Write down the midpoint of the class 20 < t <= 40.

Question 13 [1 marks]

Indices and Standard Form

Write 2.06 x 10^-3 as an ordinary number.

Question 14 [1 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (5, -2) and (5, 6).

Question 15 [1 marks]

Ratio and Proportion

Write the ratio 3:5 as a fraction in its simplest form.

Question 16 [2 marks]

Linear Algebra

Expand and simplify (x + 6)(x + 4)

Question 17 [2 marks]

Graphs and Coordinates

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

Question 18 [2 marks]

Indices and Standard Form

Work out (2 x 10^5) x (3 x 10^3). Give your answer in standard form.

Question 19 [2 marks]

Graphs and Coordinates

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

Question 20 [2 marks]

Linear Algebra

Solve 12 - 2x >= 4 Show your working.

Question 21 [2 marks]

Graphs and Coordinates

A line passes through the point (2, 5) and has a y-intercept of 1. Find the equation of the line in the form y = mx + c.

Question 22 [2 marks]

Linear Algebra

Solve 3(2x - 1) = 15 Show your working.

Question 23 [2 marks]

Area, Volume and Measures

A 1.5 litre bottle of juice is shared into glasses of 250 ml. Work out how many full glasses can be filled.

Question 24 [2 marks]

Indices and Standard Form

Here are four numbers written in standard form. 3.2 x 10^3 5.6 x 10^2 2.1 x 10^4 9.9 x 10^3 Put the numbers in order of size, starting with the smallest.

Question 25 [2 marks]

Number and Calculation

Write 84 as a product of its prime factors, giving your answer in index form.

Question 26 [2 marks]

Graphs and Coordinates

Rearrange 3x + y = 11 into the form y = mx + c and state the gradient and the y-intercept.

Question 27 [2 marks]

Statistics and Probability

Using the completed scatter graph from Question 8, describe what the correlation shows about the relationship between temperature and the number of woolly hats sold.

Question 28 [2 marks]

Quadratics

Four students each drew a table of values for y = x^2 + 2x, for -3 <= x <= 3. Only one table is correct.

Which table is correct?

Give a reason for your answer.

Question 29 [4 marks]

Area, Volume and Measures

Convert 5 metres into centimetres and into millimetres. Give both answers with units.

Write 5 m in centimetres.

Write 5 m in millimetres.

Question 30 [4 marks]

Angles and Geometrical Reasoning

Triangle ABC has vertices A(2, 0), B(5, 0) and C(2, 3). First translate the triangle by the vector (-2, 1). Then reflect the translated triangle in the x-axis. Give the coordinates of the final image of point C only.

Question 31 [4 marks]

Statistics and Probability

A market stall records the outdoor temperature (in deg C) and the number of bottles of water it sells on 9 days. The first 7 days have already been plotted on the grid. Temperature in deg C (x): 14, 16, 18, 19, 21, 22, 24 Bottles of water sold (y): 20, 24, 28, 30, 34, 36, 40 On the remaining two days, the temperature was 26 deg C with 44 bottles sold, and 28 deg C with 48 bottles sold.

Plot the remaining two points on the grid.

Draw a line of best fit on the scatter graph.

Use your line of best fit to estimate the number of bottles of water sold when the temperature is 23 deg C.

Question 32 [5 marks]

Sequences

The table shows the number of dots used to make a sequence of patterns. Pattern number (n): 1, 2, 3, 4, 5 Number of dots: 2, 7, 12, 17, ?

Complete the table by finding the number of dots in Pattern 5.

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

Find the pattern number that has 92 dots.

Question 33 [5 marks]

Graphs and Coordinates

Two courier companies charge for delivering parcels. SwiftPost charges C = 2n + 30 and ParcelGo charges C = 5n + 9, where C is the cost in pounds and n is the number of parcels. The graphs of both charges, for n from 0 to 15, are shown on the grid.

Write down the number of parcels for which the two companies charge the same amount, and state this cost.

A customer needs to send 15 parcels. By using the graphs or otherwise, determine which company is cheaper and find the difference in cost.

Question 34 [5 marks]

Linear Algebra

A car park charges according to the formula C = 2.50 + 1.20h, where C is the total cost in £ and h is the number of hours parked.

Make h the subject of the formula.

Sasha pays £8.50 to park her car. Work out how many hours she parked for.

Question 35 [6 marks]

Statistics and Probability

The Venn diagram shows information about 60 members of a drama club. S = members who can sing. D = members who can dance. Only sing = 18, only dance = 12, both sing and dance = 15, neither = 15.

Write down n(S and D).

Write down the number of members who can dance.

A member is picked at random. Find P(S or D)'.

Write down P(D and S').