IGCSE Maths Foundation Paper 1
Covers Number and Calculation, Fractions, Decimals and Percentages, Indices, Surds and Standard Form and 9 more.
Questions
Question 1 [2 marks]
Linear Equations and Inequalities
Solve x/4 - 3 = 9.
Question 2 [2 marks]
Mensuration and Vectors
A triangle has base 16 cm and perpendicular height 7 cm. Find its area.
Question 3 [3 marks]
Quadratics and Simultaneous Equations
Expand and simplify (x + 7)(x - 3).
Question 4 [3 marks]
Ratio and Proportion
A fruit squash is made from concentrate and water in the ratio 1:6.
Yuki uses 150 ml of concentrate. Find the total volume of squash she makes, in millilitres.
Question 5 [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 6 [3 marks]
Functions and Rates of Change
The function g is defined by g(x) = 2x^2 - 3.
Find g(-4).
Question 7 [3 marks]
Number and Calculation
Work out 6 + 4 x (9 - 5)^2 / 8.
Question 8 [4 marks]
Pythagoras and Trigonometry
In a right-angled triangle, the side opposite angle y is 9 cm and the side adjacent to angle y is 6.5 cm.
Find y to 1 decimal place.
Question 9 [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 10 [3 marks]
Indices, Surds and Standard Form
Simplify sqrt(8) x sqrt(18), giving your answer as an integer.
Question 11 [4 marks]
Sequences and Graphs
The straight line L has equation y = 2x - 7.
Find the equation of the line parallel to L that passes through (3, 4).
Question 12 [4 marks]
Indices, Surds and Standard Form
Work out the value of 3^-2 + 2^0, giving your answer as a single fraction.
Question 13 [4 marks]
Functions and Rates of Change
The functions f and g are defined by f(x) = x^2 - 4 and g(x) = 3x.
Find the values of x for which f(x) = g(x).
Question 14 [4 marks]
Sequences and Graphs
Find the equation of the straight line that passes through the points (1, 4) and (4, 13),
giving your answer in the form y = mx + c.
Question 15 [4 marks]
Mensuration and Vectors
A prism has cross-sectional area 22 cm^2 and length 16 cm.
Find the volume of the prism.
Question 16 [5 marks]
Fractions, Decimals and Percentages
A roll of ribbon is 5.4 m long.
Priya cuts off 1/3 of the ribbon for a project, then cuts 2/5 of what remains for a second project.
How many centimetres of ribbon are left?
Question 17 [5 marks]
Mensuration and Vectors
A window is made from a rectangle measuring 120 cm by 80 cm, topped with a semicircle whose diameter equals the 80 cm width of the rectangle.
Find the total area of the window, to the nearest cm^2.
Model solutions
| Question 1[2 marks] | |
|---|---|
| Answer or working | Marks |
| adding 3 to both sides to get x/4 = 12 | M1 |
| x = 48 | A1 |
| Question 2[2 marks] | |
|---|---|
| Answer or working | Marks |
| area = 1/2 x 16 x 7 | M1 |
| 56 cm^2 | A1 |
| Question 3[3 marks] | |
|---|---|
| Answer or working | Marks |
| at least two correct product terms | M1 |
| x^2 - 3x + 7x - 21 | M1 |
| x^2 + 4x - 21 | A1 |
| Question 4[3 marks] | |
|---|---|
| Answer or working | Marks |
| recognising 150 ml represents 1 part of the ratio | M1 |
| total parts = 1 + 6 = 7 | M1 |
| 1050 ml | A1 |
| Question 5[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 6[3 marks] | |
|---|---|
| Answer or working | Marks |
| substituting x = -4 | M1 |
| 2 x (-4)^2 | M1 |
| g(-4) = 29 | A1 |
| Final answer: 29 | |
| Question 7[3 marks] | |
|---|---|
| Answer or working | Marks |
| evaluating the bracket (9 - 5) = 4 and squaring to get 16 | M1 |
| multiplying by 4 and dividing by 8 to get 8 | M1 |
| 14 | A1 |
| Question 8[4 marks] | |
|---|---|
| Answer or working | Marks |
| using tan y = opposite/adjacent | M1 |
| tan y = 9/6.5 | M1 |
| y = tan^-1(9/6.5) | M1 |
| 54.2 degrees | A1 |
| Question 9[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 10[3 marks] | |
|---|---|
| Answer or working | Marks |
| multiplying to get sqrt(8 x 18) = sqrt(144) | M1 |
| evaluating 8 x 18 = 144 | M1 |
| 12 | A1 |
| Question 11[4 marks] | |
|---|---|
| Answer or working | Marks |
| identifying gradient 2 from a parallel line | M1 |
| using y = 2x + c | M1 |
| substituting (3, 4) to get 4 = 6 + c | M1 |
| y = 2x - 2 | A1 |
| Question 12[4 marks] | |
|---|---|
| Answer or working | Marks |
| 3^-2 = 1/9 | M1 |
| 2^0 = 1 | M1 |
| writing 1 as 9/9 | M1 |
| 10/9 | A1 |
| Question 13[4 marks] | |
|---|---|
| Answer or working | Marks |
| forming the equation x^2 - 4 = 3x | M1 |
| rearranging to x^2 - 3x - 4 = 0 | M1 |
| factorising to (x - 4)(x + 1) = 0 | M1 |
| x = 4 or x = -1 | A1 |
| Question 14[4 marks] | |
|---|---|
| Answer or working | Marks |
| finding the gradient (13 - 4)/(4 - 1) = 3 | M1 |
| substituting (1, 4) into y = 3x + c | M1 |
| solving to find c = 1 | M1 |
| y = 3x + 1 | A1 |
| Question 15[4 marks] | |
|---|---|
| Answer or working | Marks |
| volume = cross-sectional area x length | M1 |
| 22 x 16 | M1 |
| 352 | A1 |
| cm^3 | B1 |
| Final answer: 352 cm^3 | |
| Question 16[5 marks] | |
|---|---|
| Answer or working | Marks |
| finding 2/3 of 5.4 = 3.6 m remaining after the first cut | M1 |
| finding 2/5 of 3.6 = 1.44 m | M1 |
| subtracting to leave 3.6 - 1.44 = 2.16 m | M1 |
| converting 2.16 m to centimetres | M1 |
| 216 cm | A1 |
| Question 17[5 marks] | |
|---|---|
| Answer or working | Marks |
| the rectangle area = 120 x 80 = 9600 cm^2 | M1 |
| the semicircle radius = 40 cm | M1 |
| the semicircle area = 1/2 x pi x 40^2 | M1 |
| the semicircle area = 2513.27... cm^2 | A1 |
| the total area = 12113 cm^2 | A1 |
| Final answer: 12113 cm^2 | |