Cambridge AS Level Mathematics - Pure 1. All Exam Questions and Correct
Answers | Graded A+ | 2025/2026 Update|
4- Evaluate.
(-8)^(2/3)
1/4 - Evaluate.
(-8)^(-2/3)
2/3 - Evaluate.
(9/4)^(-1/2)
x=6- Find x.
7⁸ ÷ 7ˣ = 49
x=6- Find x.
(6⁵ × 6ˣ) ÷ 36 = 6⁹
x=9- Find x.
(5⁷ × 5⁴) ÷ 5ˣ = 25
20 - Evaluate (2√5)²
x = -7 or 5 - Solve the quadratic equation by factorisation
x² + 2x - 35 = 0
,x = 0 or 4 - Solve the quadratic equation by factorisation
5x² = 20x
49cm² - A piece of card has a length of (2x - 1)cm and a width of (x + 2)cm. A square of
side xcm is removed from the card. The area of the card that is left is 68cm². Find the area of the
card that has been removed.
x = (-b ± √b² - 4ac) / 2a - What is the quadratic formula?
x = -(5/2) - Solve the quadratic equation
(2x² + 5x + 3) / (x² + 3x + 2) = 4
x≥2- Solve
2x + 7 ≤ 8x - 5
x ≤ 2/5 - Solve
4x - 7(2x - 1) ≥ 3
x≤-1- Solve
(4 + x) / 3 ≤ 1 - 5(1 + x)
-5 ≤ x ≤ 1/2 - Solve and sketch the inequality
(5 + x)(1 - 2x) ≥ 0
x ≤ -7/2 or x ≥ -4/5 - Solve and sketch the inequality
10x² + 43x + 28 ≥ 0
x ≤ 2, x ≥ 6 - Solve and sketch the inequality
, (x² + 12) / 2 ≥ 4x
(x + b/2)² - (b/2)² + c - Complete the square
x² + bx + c
(x - 5)² - 5 - Write in the form (x + p)² + q
x² - 10x + 20
x = 2 ± 2√3 - Complete the square to find x
x² - 4x - 8 = 0
x = 6 ± 0.5√170 - Complete the square to find x
4x² - 48x - 26
x = 0.42 or 1.58 - Solve using the quadratic formula to 2 decimal places.
3x² = 6x - 2
x = (-5 ± √57) / 4 - Solve using the quadratic formula.
2x² -4 + 5x = 0
(-1 - √5) / 2 < x < (-1 + √5) / 2 - Solve using the quadratic formula.
x² < 1 - x
3- How many significant figures should your final answer in the exam have?
x = ± 1.79 - Solve using the quadratic formula.
To 3 sig figures.
Answers | Graded A+ | 2025/2026 Update|
4- Evaluate.
(-8)^(2/3)
1/4 - Evaluate.
(-8)^(-2/3)
2/3 - Evaluate.
(9/4)^(-1/2)
x=6- Find x.
7⁸ ÷ 7ˣ = 49
x=6- Find x.
(6⁵ × 6ˣ) ÷ 36 = 6⁹
x=9- Find x.
(5⁷ × 5⁴) ÷ 5ˣ = 25
20 - Evaluate (2√5)²
x = -7 or 5 - Solve the quadratic equation by factorisation
x² + 2x - 35 = 0
,x = 0 or 4 - Solve the quadratic equation by factorisation
5x² = 20x
49cm² - A piece of card has a length of (2x - 1)cm and a width of (x + 2)cm. A square of
side xcm is removed from the card. The area of the card that is left is 68cm². Find the area of the
card that has been removed.
x = (-b ± √b² - 4ac) / 2a - What is the quadratic formula?
x = -(5/2) - Solve the quadratic equation
(2x² + 5x + 3) / (x² + 3x + 2) = 4
x≥2- Solve
2x + 7 ≤ 8x - 5
x ≤ 2/5 - Solve
4x - 7(2x - 1) ≥ 3
x≤-1- Solve
(4 + x) / 3 ≤ 1 - 5(1 + x)
-5 ≤ x ≤ 1/2 - Solve and sketch the inequality
(5 + x)(1 - 2x) ≥ 0
x ≤ -7/2 or x ≥ -4/5 - Solve and sketch the inequality
10x² + 43x + 28 ≥ 0
x ≤ 2, x ≥ 6 - Solve and sketch the inequality
, (x² + 12) / 2 ≥ 4x
(x + b/2)² - (b/2)² + c - Complete the square
x² + bx + c
(x - 5)² - 5 - Write in the form (x + p)² + q
x² - 10x + 20
x = 2 ± 2√3 - Complete the square to find x
x² - 4x - 8 = 0
x = 6 ± 0.5√170 - Complete the square to find x
4x² - 48x - 26
x = 0.42 or 1.58 - Solve using the quadratic formula to 2 decimal places.
3x² = 6x - 2
x = (-5 ± √57) / 4 - Solve using the quadratic formula.
2x² -4 + 5x = 0
(-1 - √5) / 2 < x < (-1 + √5) / 2 - Solve using the quadratic formula.
x² < 1 - x
3- How many significant figures should your final answer in the exam have?
x = ± 1.79 - Solve using the quadratic formula.
To 3 sig figures.
