Foundation Core B
Foundation fluency with graphs, sequences, compound measures and shape.
Questions
Question 1 [1 marks]
Angles and Geometrical Reasoning
Which of these gives the sum of the interior angles, in degrees, of a polygon with n sides?
Question 2 [1 marks]
Area, Volume and Measures
Convert 3.5 m to cm.
Question 3 [2 marks]
Graphs and Coordinates
For each equation, write down the gradient and the y-intercept of the line.
y = 5x - 2
y = -3x + 7
Question 4 [2 marks]
Fractions, Decimals and Percentages
Aisha says that 1/3 is bigger than 3/10. Decide whether Aisha is correct. You must show working to support your decision.
Question 5 [2 marks]
Ratio and Proportion
Write the ratio 9:36 in the form 1:n.
Question 6 [2 marks]
Linear Algebra
Solve x / (-3) = 6
Question 7 [2 marks]
Number and Calculation
Two numbers are each given correct to the nearest whole number: p = 14 and q = 9. Work out the lower bound of p + q.
Question 8 [3 marks]
Sequences
Three sequences are shown below. Sequence A: 7, 11, 15, 19 Sequence B: 4, 12, 36, 108 Sequence C: 3, 6, 11, 18
State whether Sequence A is arithmetic, geometric, or neither of these. Give a reason for your answer.
State whether Sequence B is arithmetic, geometric, or neither of these. Give a reason for your answer.
State whether Sequence C is arithmetic, geometric, or neither of these. Give a reason for your answer.
Question 9 [5 marks]
Statistics and Probability
A pictogram shows the number of pupils who chose each activity for a school trip day, using the key 1 symbol = 1 pupil. Alton Towers: 5 symbols. London Zoo: 3 symbols. Warwick Castle: 2 symbols. Chessington: 6 symbols.
Write down the number of pupils who chose Warwick Castle.
List the four activities in order of popularity, starting with the most popular.
Work out the total number of pupils who took part in the survey.
Question 10 [1 marks]
Number and Calculation
Work out (-3) x 4.
Question 11 [1 marks]
Angles and Geometrical Reasoning
A solid has stacks on a 2 by 2 grid with heights (in unit cubes) Front-left 2, Front-right 1, Back-left 1, Back-right 1. How many unit cubes make up the solid in total?
Question 12 [1 marks]
Graphs and Coordinates
Which quadrant contains the point C with coordinates (-6, 2)?
Question 13 [2 marks]
Area, Volume and Measures
Trapezium 1 has parallel sides of length 8 cm and 15 cm. Trapezium 2 is mathematically similar to trapezium 1. The side in trapezium 2 corresponding to the 8 cm side has length 5.6 cm.
Question 14 [2 marks]
Number and Calculation
Estimate 246 × 78 by rounding each number to 1 significant figure before multiplying.
Question 15 [3 marks]
Angles and Geometrical Reasoning
Triangle ABC has side lengths AB = 7 cm, BC = 8 cm and AC = 9 cm. Construct the perpendicular bisectors of two sides to find the circumcentre. Calculate the circumradius (to 3 significant figures).
Question 16 [3 marks]
Fractions, Decimals and Percentages
The population of a small town is 1200. It falls by 5% one year and then rises by 10% the next year. Work out the population after these two changes. Give your answer to the nearest whole person.
Question 17 [4 marks]
Ratio and Proportion
A lorry travels 240 km in 3 hours. Part (a): Work out its average speed in km/h. Part (b): The lorry then continues at the same speed for 2 hours. Work out the extra distance it covers.
Work out the average speed.
Work out the extra distance covered in 2 hours at the same speed.
Question 18 [4 marks]
Number and Calculation
A photographer charges a base fee of £45 plus £12 per hour. Noah hires the photographer for 3.5 hours. (a) Work out the total cost. (b) Work out the average cost per hour, correct to the nearest penny.
Question 19 [4 marks]
Area, Volume and Measures
A vertical stick of height 1.2 m casts a shadow 2 m long. At the same time, a nearby vertical flagpole casts a shadow 12 m long. The stick and its shadow, and the flagpole and its shadow, can be modelled as two similar right-angled triangles.
Explain why the two triangles are similar.
Work out the height of the flagpole. Give your answer in metres.
Question 20 [6 marks]
Ratio and Proportion
A car being driven at a constant average speed takes 3 hours to complete a journey when its average speed is 60 mph. The time taken, T hours, for the journey is inversely proportional to the average speed, S mph.
Find a formula for T in terms of S.
Work out the time taken for the same journey if the average speed is 40 mph. Give your answer in hours and minutes.
Question 21 [7 marks]
Statistics and Probability
A library shelf holds 8 fiction books and 12 non-fiction books only. Sophie picks two books from the shelf at random, one after another, without replacement.
Complete the probability tree diagram, writing each missing probability as a fraction.
Calculate the probability that both books are fiction.
Calculate the probability that exactly one of the two books is fiction.
Question 22 [2 marks]
Number and Calculation
Work out (-8) + 15 - 6.
Model solutions
| Question 1[1 mark] | |
|---|---|
| Answer or working | Marks |
| B | B1cao |
| Final answer: B) (n - 2) x 180 | |
| Question 2[1 mark] | |
|---|---|
| Answer or working | Marks |
| 350 | B1cao |
| Final answer: 350 cm | |
| Question 3[2 marks] | |
|---|---|
| Answer or working | Marks |
| gradient = 5 and y-intercept = (0, -2), both correct | B1 |
| gradient = -3 and y-intercept = (0, 7), both correct | B1 |
| Final answer: Gradient = 5, y-intercept = (0, -2) | Gradient = -3, y-intercept = (0, 7) | |
| Question 4[2 marks] | |
|---|---|
| Answer or working | Marks |
| correct working, e.g. converting to a common denominator: 1/3 = 10/30 and 3/10 = 9/30 | B1 |
| correct conclusion that Aisha is correct, since 10/30 > 9/30 | B1 |
| Final answer: Aisha is correct, since 1/3 = 10/30 and 3/10 = 9/30, and 10/30 > 9/30. | |
| Question 5[2 marks] | |
|---|---|
| Answer or working | Marks |
| divide both parts by 9 | M1oe |
| 1:4 | A1cao |
| Question 6[2 marks] | |
|---|---|
| Answer or working | Marks |
| both sides multiplied by -3 | M1oe |
| x = -18 | A1cao |
| Question 7[2 marks] | |
|---|---|
| Answer or working | Marks |
| lower bound of p = 13.5 and lower bound of q = 8.5 | M1oe |
| 22 | A1cao |
| Question 8[3 marks] | |
|---|---|
| Answer or working | Marks |
| arithmetic, since the terms have a common difference of 4 | B1oe |
| geometric, since the terms have a common ratio of 3 | B1oe |
| neither, since the differences (3, 5, 7) are not constant and the ratios are not constant | B1oe |
| Final answer: Arithmetic (common difference of 4) | Geometric (common ratio of 3) | Neither (it is a quadratic sequence) | |
| Question 9[5 marks] | |
|---|---|
| Answer or working | Marks |
| 2 | B1cao |
| at least three activities correctly placed relative to each other | M1oe |
| Chessington, Alton Towers, London Zoo, Warwick Castle | A1cao |
| 5 + 3 + 2 + 6 | M1oe |
| 16 | A1cao |
| Final answer: 2 | Chessington, Alton Towers, London Zoo, Warwick Castle | 16 | |
| Question 10[1 mark] | |
|---|---|
| Answer or working | Marks |
| -12 | B1cao |
| Question 11[1 mark] | |
|---|---|
| Answer or working | Marks |
| 5 | B1cao |
| Final answer: 5 (2 + 1 + 1 + 1 = 5 unit cubes). | |
| Question 12[1 mark] | |
|---|---|
| Answer or working | Marks |
| Quadrant II or Q2 | B1oe |
| Final answer: Quadrant II | |
| Question 13[2 marks] | |
|---|---|
| Answer or working | Marks |
| scale factor = 5.6/8 oe (= 0.7) | M1 |
| 10.5 (cm) | A1cao |
| Final answer: 10.5 cm | |
| Question 14[2 marks] | |
|---|---|
| Answer or working | Marks |
| round 246->200 and 78->80 to 1 s.f. and multiply | M1oe |
| 16000 | A1cao |
| Question 15[3 marks] | |
|---|---|
| Answer or working | Marks |
| use Heron to find area: s = 12, area = sqrt(12(12-7)(12-8)(12-9)) = sqrt(720) | M1 |
| use circumradius formula R = abc/(4*area) with a=8, b=9, c=7 | M1 |
| R = 7*8*9/(4*sqrt(720)) approx 4.70 cm | A1awrt |
| Final answer: Circumradius R approx 4.70 cm (to 3 s.f.). Computation: s = 12, area = sqrt(720) approx 26.8328, R = 504/(4*26.8328) approx 4.698 -> 4.70. | |
| Question 16[3 marks] | |
|---|---|
| Answer or working | Marks |
| apply decrease: 1200 x 0.95 = 1140 | M1 |
| apply increase: 1140 x 1.10 = 1254 | M1 |
| 1254 people | A1cao |
| Question 17[4 marks] | |
|---|---|
| Answer or working | Marks |
| use speed = distance/time, 240/3 | M1 |
| 80 km/h | A1cao |
| distance = speed x time, 80 x 2 | M1 |
| 160 km | A1cao |
| Final answer: 80 km/h | 160 km | |
| Question 18[4 marks] | |
|---|---|
| Answer or working | Marks |
| calculates 45 + 12 × 3.5 | M1 |
| £87.00 | A1cao |
| divides total cost by 3.5 correctly | M1 |
| £24.86 cao (rounded to nearest penny) | A1 |
| Final answer: £87.00 | £24.86 per hour (to nearest penny). | |
| Question 19[4 marks] | |
|---|---|
| Answer or working | Marks |
| both triangles have a right angle (object vertical to horizontal ground) and the same angle of elevation of the sun (parallel light rays), so they are similar (AA) | B1 |
| scale factor = 12/2 oe (= 6) | M1 |
| 1.2 x their scale factor | M1 |
| 7.2 (m) | A1cao |
| Final answer: a) AA similarity (right angle and equal angle of elevation) b) 7.2 m | |
| Question 20[6 marks] | |
|---|---|
| Answer or working | Marks |
| T = k/S oe seen | M1 |
| 3 = k/60 solved (dependent on previous M1) | dM1 |
| T = 180/S | A1oe |
| 180/40 (ft their formula) | M1 |
| 4.5 hours | A1oe |
| 4 hours 30 minutes | B1ft |
| Final answer: T = 180/S | 4 hours 30 minutes | |
| Question 21[7 marks] | |
|---|---|
| Answer or working | Marks |
| 7/19 and 12/19 on the branches after Fiction | B1 |
| 8/19 and 11/19 on the branches after Non-fiction | B1 |
| 8/20 x 7/19 | M1 |
| 14/95 oe (e.g. 56/380, awrt 0.147) | A1 |
| 8/20 x 12/19 (or 12/20 x 8/19) for one correct route | M1 |
| 8/20 x 12/19 + 12/20 x 8/19 (both routes added) | M1 |
| 48/95 oe (e.g. 192/380, awrt 0.505) | A1 |
| Final answer: After Fiction: Fiction 7/19, Non-fiction 12/19. After Non-fiction: Fiction 8/19, Non-fiction 11/19 | 14/95 | 48/95 | |
| Question 22[2 marks] | |
|---|---|
| Answer or working | Marks |
| -8 + 15 (= 7) (oe), or equivalent complete method | M1 |
| 1 | A1cao |