IGCSE Maths Foundation Short Paper A
Covers Number and Calculation, Fractions, Decimals and Percentages, Indices, Surds and Standard Form and 3 more.
Questions
Question 1 [2 marks]
Number and Calculation
A stationery shop orders 34 boxes of pens. Each box contains 48 pens.
The shop already has 156 pens in stock. Work out the total number of pens now in the shop.
Question 2 [2 marks]
Indices, Surds and Standard Form
Evaluate 25^(1/2) + 8^(1/3).
Question 3 [3 marks]
Fractions, Decimals and Percentages
In a test, Freya scored 42 out of 56. Express her score as a percentage.
Question 4 [3 marks]
Quadratics and Simultaneous Equations
Expand and simplify (x + 7)(x - 3).
Question 5 [3 marks]
Linear Equations and Inequalities
Expand and simplify 3(2x - 5) + 4(x + 6).
Question 6 [4 marks]
Ratio and Proportion
A bag of 360 sweets is shared between Priya, Sam and Tom in the ratio 4:5:9.
Find the difference between Tom's share and Priya's share.
Question 7 [3 marks]
Linear Equations and Inequalities
Solve the inequality 4x + 7 < 2x + 19.
Question 8 [3 marks]
Indices, Surds and Standard Form
Simplify (x^7 y^3)/(x^3 y^-2).
Give your answer using positive indices.
Question 9 [4 marks]
Ratio and Proportion
A map has a scale of 1:20000.
The distance between two farms on the map is 5.4 cm.
Find the real distance between the farms in kilometres.
Question 10 [4 marks]
Fractions, Decimals and Percentages
A meal at a restaurant costs 34.65 pounds before a 15% service charge is added.
Find the total cost of the meal, giving your answer to the nearest penny.
Question 11 [4 marks]
Indices, Surds and Standard Form
Work out the value of 3^-2 + 2^0, giving your answer as a single fraction.
Question 12 [5 marks]
Quadratics and Simultaneous Equations
Solve 3x^2 + 11x - 4 = 0 by factorising.
Model solutions
| Question 1[2 marks] | |
|---|---|
| Answer or working | Marks |
| 34 x 48 = 1632 | M1 |
| 1788 pens | A1 |
| Question 2[2 marks] | |
|---|---|
| Answer or working | Marks |
| 25^(1/2) = 5 and 8^(1/3) = 2 | M1 |
| 7 | A1 |
| Question 3[3 marks] | |
|---|---|
| Answer or working | Marks |
| finding 42/56 | M1 |
| converting to a decimal, 0.75 | M1 |
| 75% | A1 |
| Question 4[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 5[3 marks] | |
|---|---|
| Answer or working | Marks |
| expanding to 6x - 15 + 4x + 24 | M1 |
| collecting like x terms and constants | M1 |
| 10x + 9 | A1 |
| Question 6[4 marks] | |
|---|---|
| Answer or working | Marks |
| total parts = 4 + 5 + 9 = 18 | M1 |
| one part = 360 / 18 = 20 | M1 |
| Tom's share = 9 x 20 = 180 and Priya's share = 4 x 20 = 80 | M1 |
| 100 sweets | A1 |
| Question 7[3 marks] | |
|---|---|
| Answer or working | Marks |
| collecting terms in x on one side, such as 2x + 7 < 19 | M1 |
| 2x < 12 | M1 |
| x < 6 | A1 |
| Question 8[3 marks] | |
|---|---|
| Answer or working | Marks |
| subtracting powers of x to get x^4 | M1 |
| subtracting powers of y to get y^5 | M1 |
| x^4 y^5 | A1 |
| Question 9[4 marks] | |
|---|---|
| Answer or working | Marks |
| multiplying 5.4 by 20000 | M1 |
| 108000 cm | A1 |
| converting cm to km by dividing by 100000 | M1 |
| 1.08 km | A1 |
| Question 10[4 marks] | |
|---|---|
| Answer or working | Marks |
| finding 15% of 34.65 | M1 |
| 15% of 34.65 = 5.1975 | M1 |
| adding to the original price | M1 |
| 39.85 pounds (nearest penny) | A1 |
| Final answer: 39.85 pounds | |
| Question 11[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 12[5 marks] | |
|---|---|
| Answer or working | Marks |
| finding two numbers with product -12 (3 x -4) and sum 11 | M1 |
| identifying 12 and -1 | M1 |
| factorising to (3x - 1)(x + 4) = 0 | M1 |
| x = 1/3 | A1 |
| x = -4 | A1 |
| Final answer: x = 1/3 or x = -4 | |