IGCSE Maths Foundation Short Paper B
Covers Functions and Rates of Change, Sequences and Graphs, Angles, Polygons and Circle Theorems and 3 more.
Questions
Question 1 [2 marks]
Functions and Rates of Change
The function f is defined by f(x) = 3x - 5.
Find f(4).
Question 2 [2 marks]
Mensuration and Vectors
A triangle has base 16 cm and perpendicular height 7 cm. Find its area.
Question 3 [2 marks]
Pythagoras and Trigonometry
A right-angled triangle has hypotenuse 26 cm and one shorter side 10 cm.
Find the length of the other shorter side.
Question 4 [3 marks]
Sequences and Graphs
Find the midpoint of the line segment joining the points (2, -5) and (8, 3).
Question 5 [3 marks]
Pythagoras and Trigonometry
A right-angled triangle has shorter sides 9 cm and 12 cm.
Find the length of the hypotenuse.
Question 6 [4 marks]
Angles, Polygons and Circle Theorems
Three angles meet at a point. One angle is 130 degrees, another is 3x degrees and the third is 2x degrees.
Find the value of x, then state the size of the smallest of the three angles at the point.
Question 7 [3 marks]
Statistics and Probability
The numbers of goals scored by a football team in six matches are 2, 0, 3, 1, 4 and 2.
Find the mean and the range of the number of goals.
Question 8 [3 marks]
Angles, Polygons and Circle Theorems
A regular polygon has each exterior angle equal to 15 degrees.
Find the number of sides of the polygon.
Question 9 [4 marks]
Functions and Rates of Change
The function f is defined by f(x) = x^2 - 2x.
Find the value of f(3) x f(-3).
Question 10 [4 marks]
Mensuration and Vectors
A circular pond has radius 6.5 m.
Find its circumference to 1 decimal place.
Question 11 [5 marks]
Statistics and Probability
A biased six-sided dice is rolled 200 times.
The number 6 is rolled 55 times.
Find the relative frequency of rolling a 6, and use it to estimate how many times a 6 would be rolled in 600 rolls.
Question 12 [5 marks]
Pythagoras and Trigonometry
A cuboid has length 8 cm, width 5 cm and height 6 cm.
Find the length of the diagonal that runs from one corner of the cuboid to the opposite corner, to 1 decimal place.
Model solutions
| Question 1[2 marks] | |
|---|---|
| Answer or working | Marks |
| substituting x = 4 into f(x) | M1 |
| f(4) = 7 | A1 |
| Final answer: 7 | |
| Question 2[2 marks] | |
|---|---|
| Answer or working | Marks |
| area = 1/2 x 16 x 7 | M1 |
| 56 cm^2 | A1 |
| Question 3[2 marks] | |
|---|---|
| Answer or working | Marks |
| using b^2 = c^2 - a^2, giving 26^2 - 10^2 = 576 | M1 |
| 24 cm | A1 |
| Question 4[3 marks] | |
|---|---|
| Answer or working | Marks |
| adding the x-coordinates and dividing by 2 | M1 |
| adding the y-coordinates and dividing by 2 | M1 |
| (5, -1) | A1 |
| Question 5[3 marks] | |
|---|---|
| Answer or working | Marks |
| using a^2 + b^2 = c^2 | M1 |
| 9^2 + 12^2 = 225 | M1 |
| 15 cm | A1 |
| Question 6[4 marks] | |
|---|---|
| Answer or working | Marks |
| using angles around a point sum to 360 degrees | M1 |
| 130 + 3x + 2x = 360 | M1 |
| solving to x = 46 | M1 |
| the smallest angle = 2 x 46 = 92 degrees | A1 |
| Final answer: x = 46; smallest angle = 92 degrees | |
| Question 7[3 marks] | |
|---|---|
| Answer or working | Marks |
| summing the six values to get 12 | M1 |
| mean = 2 | A1 |
| range = 4 | A1 |
| Final answer: mean 2, range 4 | |
| Question 8[3 marks] | |
|---|---|
| Answer or working | Marks |
| exterior angles of a polygon sum to 360 degrees | M1 |
| 360 divided by 15 | M1 |
| 24 sides | A1 |
| Question 9[4 marks] | |
|---|---|
| Answer or working | Marks |
| f(3) = 9 - 6 = 3 | M1 |
| f(-3) = 9 + 6 = 15 | M1 |
| multiplying the two values | M1 |
| 45 | A1 |
| Question 10[4 marks] | |
|---|---|
| Answer or working | Marks |
| using circumference = 2 pi r | M1 |
| 2 x pi x 6.5 | M1 |
| 40.840... before rounding | M1 |
| 40.8 m | A1 |
| Question 11[5 marks] | |
|---|---|
| Answer or working | Marks |
| relative frequency = 55/200 | M1 |
| 0.275 | A1 |
| using the relative frequency as an estimate of probability | M1 |
| 0.275 x 600 | M1 |
| 165 times | A1 |
| Final answer: relative frequency = 0.275, estimated 165 times in 600 rolls | |
| Question 12[5 marks] | |
|---|---|
| Answer or working | Marks |
| using the 3D Pythagoras formula d = sqrt(l^2 + w^2 + h^2) | M1 |
| 8^2 + 5^2 + 6^2 = 125 | M1 |
| taking the square root of 125 | M1 |
| 11.18033... | A1 |
| 11.2 cm | A1 |