Foundation Basics A

Question 1 [1 marks]

Linear Algebra

Which of these expressions is equivalent to 3(2x - 5)?

Question 2 [2 marks]

Angles and Geometrical Reasoning

Rectangle P has vertices at (2, 1), (5, 1), (5, 3) and (2, 3). Rectangle P is reflected in the x-axis to give rectangle Q.

Question 3 [3 marks]

Ratio and Proportion

A shop sells notebooks in packs. Pack A: 4 notebooks for GBP 3.20 Pack B: 6 notebooks for GBP 4.50

Work out the cost of one notebook from Pack A.

Work out the cost of one notebook from Pack B.

State which pack is better value for money. Give a reason for your answer.

Question 4 [4 marks]

Number and Calculation

State whether each statement about the number 84 is True or False.

84 is a multiple of 9.

84 is a factor of 168.

84 is a prime number.

The Highest Common Factor of 84 and 36 is 12.

Question 5 [5 marks]

Statistics and Probability

The times, in seconds, taken by 11 sprinters to run 100m in a school athletics trial were recorded: 11.8, 12.3, 13.1, 11.5, 12.9, 13.4, 11.5, 12.0, 13.8, 12.6, 11.2

Draw an ordered stem and leaf diagram to show this information. Use the whole number of seconds as the stem and the first decimal digit as the leaf. Include a key.

Find the median time.

Question 6 [1 marks]

Number and Calculation

Work out 12 x 0.8.

Question 7 [2 marks]

Linear Algebra

Expand and simplify (x - 3)(x - 8)

Question 8 [2 marks]

Number and Calculation

A school trip needs to transport 134 students. Each minibus can carry 15 students. Work out the least number of minibuses needed to transport all the students.

Question 9 [3 marks]

Angles and Geometrical Reasoning

A rectangular lawn is shown on a garden plan with scale 1:250. On the plan the lawn measures 3.2 cm by 2 cm. Turf costs £4.50 per square metre. Work out the total cost of turfing the lawn.

Question 10 [3 marks]

Number and Calculation

A car park at a retail park has 850 spaces. At 9am, 612 cars are parked in the car park. During the morning, 89 cars leave and 143 more cars arrive. Work out how many empty spaces there are in the car park after these changes.

Question 11 [5 marks]

Statistics and Probability

Chidi rolls a six-sided dice 60 times and scores a six 14 times. Aisha rolls an identical dice 500 times and scores a six 79 times.

Work out the relative frequency of scoring a six in each experiment, giving your answers as decimals to 3 significant figures.

State, with a reason, whose experiment gives the more reliable estimate of the probability of scoring a six.

Kwame says: 'Chidi's dice must be biased, because his relative frequency of 14 out of 60 is higher than Aisha's.' Explain why Kwame's conclusion is not necessarily correct.

Question 12 [4 marks]

Fractions, Decimals and Percentages

Write down the single decimal multiplier for each of the following percentage changes.

an increase of 3%

a decrease of 5%

an increase of 12%

a decrease of 40%

Question 13 [5 marks]

Statistics and Probability

On any given day, the probability that Jamal passes his driving theory mock test is 0.8. The probability that he passes his practical mock test is 0.75. The results of the two mock tests are independent of each other.

Find the probability that Jamal passes both mock tests.

Find the probability that Jamal passes exactly one of the two mock tests.