IGCSE Maths Higher Short Paper A
Covers Number and Calculation, Fractions, Decimals and Percentages, Indices, Surds and Standard Form and 3 more.
Questions
Question 1 [3 marks]
Number and Calculation
Work out 6 + 4 x (9 - 5)^2 / 8.
Question 2 [5 marks]
Quadratics and Simultaneous Equations
Solve 2x^2 - 5x - 12 = 0 by factorising.
Question 3 [3 marks]
Linear Equations and Inequalities
Solve the inequality 15 - 3x > 6.
Question 4 [4 marks]
Fractions, Decimals and Percentages
Write these in order of size, starting with the smallest: 5/8, 0.62, 59%.
Question 5 [3 marks]
Linear Equations and Inequalities
Solve the inequality 4x + 7 < 2x + 19.
Question 6 [5 marks]
Fractions, Decimals and Percentages
A bank account pays simple interest at a rate of 3.2% per year.
2400 pounds is invested for 4 years.
Find the total simple interest earned, and find the value of the investment at the end of the 4 years.
Question 7 [5 marks]
Number and Calculation
P = 6.4 x 10^5 and Q = 3.7 x 10^4.
Work out P + Q, giving your answer in standard form.
Question 8 [6 marks]
Ratio and Proportion
Two cyclists start 63 km apart and cycle towards each other along the same road.
Cyclist A travels at 15 km/h and cyclist B travels at 12 km/h.
Find how long it takes for the two cyclists to meet, giving your answer in hours and minutes.
Question 9 [6 marks]
Indices, Surds and Standard Form
Rationalise the denominator of 39/(4 - sqrt(3)).
Give your answer in the form a + b sqrt(3), where a and b are integers.
Model solutions
| Question 1[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 2[5 marks] | |
|---|---|
| Answer or working | Marks |
| finding two numbers with product -24 and sum -5 | M1 |
| identifying -8 and 3 | M1 |
| factorising to (2x + 3)(x - 4) = 0 | M1 |
| x = -3/2 | A1 |
| x = 4 | A1 |
| Final answer: x = -3/2 or x = 4 | |
| Question 3[3 marks] | |
|---|---|
| Answer or working | Marks |
| subtracting 15 from both sides to get -3x > -9 | M1 |
| dividing both sides by -3 and reversing the inequality | M1 |
| x < 3 | A1 |
| Question 4[4 marks] | |
|---|---|
| Answer or working | Marks |
| converting 5/8 to a decimal, 0.625 | M1 |
| converting 59% to a decimal, 0.59 | M1 |
| comparing all three as decimals: 0.59, 0.62, 0.625 | M1 |
| 59%, 0.62, 5/8 | A1 |
| Question 5[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 6[5 marks] | |
|---|---|
| Answer or working | Marks |
| finding 3.2% of 2400 | M1 |
| 3.2% of 2400 = 76.8 | M1 |
| multiplying by 4 years | M1 |
| total interest = 307.20 pounds | A1 |
| final value = 2707.20 pounds | A1 |
| Final answer: interest = 307.20 pounds, final value = 2707.20 pounds | |
| Question 7[5 marks] | |
|---|---|
| Answer or working | Marks |
| converting to the same power of 10, such as P = 64 x 10^4 | M1 |
| identifying Q = 3.7 x 10^4 | M1 |
| 64 x 10^4 + 3.7 x 10^4 = 67.7 x 10^4 | M1 |
| 677000 | A1 |
| 6.77 x 10^5 | A1 |
| Question 8[6 marks] | |
|---|---|
| Answer or working | Marks |
| combined speed = 15 + 12 = 27 km/h | M1 |
| time = distance / combined speed | M1 |
| 63 / 27 = 7/3 hours | M1 |
| converting 7/3 hours to 2 1/3 hours | M1 |
| 2 hours | A1 |
| 20 minutes | A1 |
| Final answer: 2 hours 20 minutes | |
| Question 9[6 marks] | |
|---|---|
| Answer or working | Marks |
| multiplying numerator and denominator by (4 + sqrt(3)) | M1 |
| the denominator (4 - sqrt(3))(4 + sqrt(3)) = 16 - 3 | M1 |
| denominator = 13 | A1 |
| the numerator 39(4 + sqrt(3)) = 156 + 39 sqrt(3) | M1 |
| dividing both terms by 13 | M1 |
| 12 + 3 sqrt(3) | A1 |