Worked Solutions Manual – Cambridge
International AS & A Level Mathematics:
Probability & Statistics 1 (P1) | Dean
Chalmers | Cambridge Elevate Edition
4 - answer-Evaluate.
(-8)^(2/3)
1/4 - answer-Evaluate.
(-8)^(-2/3)
2/3 - answer-Evaluate.
(9/4)^(-1/2)
x = 6 - answer-Find x.
7⁸ ÷ 7ˣ = 49
x = 6 - answer-Find x.
(6⁵ × 6ˣ) ÷ 36 = 6⁹
x = 9 - answer-Find x.
(5⁷ × 5⁴) ÷ 5ˣ = 25
1
,20 - answer-Evaluate (2√5)²
x = -7 or 5 - answer-Solve the quadratic equation by factorisation
x² + 2x - 35 = 0
x = 0 or 4 - answer-Solve the quadratic equation by factorisation
5x² = 20x
49cm² - answer-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 - answer-What is the quadratic formula?
x = -(5/2) - answer-Solve the quadratic equation
(2x² + 5x + 3) / (x² + 3x + 2) = 4
x ≥ 2 - answer-Solve
2x + 7 ≤ 8x - 5
x ≤ 2/5 - answer-Solve
4x - 7(2x - 1) ≥ 3
x ≤ - 1 - answer-Solve
2
,(4 + x) / 3 ≤ 1 - 5(1 + x)
-5 ≤ x ≤ 1/2 - answer-Solve and sketch the inequality
(5 + x)(1 - 2x) ≥ 0
x ≤ -7/2 or x ≥ -4/5 - answer-Solve and sketch the inequality
10x² + 43x + 28 ≥ 0
x ≤ 2, x ≥ 6 - answer-Solve and sketch the inequality
(x² + 12) / 2 ≥ 4x
(x + b/2)² - (b/2)² + c - answer-Complete the square
x² + bx + c
(x - 5)² - 5 - answer-Write in the form (x + p)² + q
x² - 10x + 20
x = 2 ± 2√3 - answer-Complete the square to find x
x² - 4x - 8 = 0
x = 6 ± 0.5√170 - answer-Complete the square to find x
4x² - 48x - 26
x = 0.42 or 1.58 - answer-Solve using the quadratic formula to 2 decimal places.
3
, 3x² = 6x - 2
x = (-5 ± √57) / 4 - answer-Solve using the quadratic formula.
2x² -4 + 5x = 0
(-1 - √5) / 2 < x < (-1 + √5) / 2 - answer-Solve using the quadratic formula.
x² < 1 - x
3 - answer-How many significant figures should your final answer in the exam have?
x = ± 1.79 - answer-Solve using the quadratic formula.
To 3 sig figures.
2x⁸ - 20x⁴ - 7 = 0
x = (-b ± √b² - 4ac) / 2a - answer-Complete the square to find x
ax² + bx + c = 0
(draw the graph) - answer-Show that x² + 8x + 16 ≥ 0 for all values of x
(delta) - answer-What is the symbol for the discriminant?
(delta) = b² - 4ac - answer-What is the equation for the discriminant?
(delta) = -23
There are no real roots - answer-Work out the discriminant and determine how many roots the
4
International AS & A Level Mathematics:
Probability & Statistics 1 (P1) | Dean
Chalmers | Cambridge Elevate Edition
4 - answer-Evaluate.
(-8)^(2/3)
1/4 - answer-Evaluate.
(-8)^(-2/3)
2/3 - answer-Evaluate.
(9/4)^(-1/2)
x = 6 - answer-Find x.
7⁸ ÷ 7ˣ = 49
x = 6 - answer-Find x.
(6⁵ × 6ˣ) ÷ 36 = 6⁹
x = 9 - answer-Find x.
(5⁷ × 5⁴) ÷ 5ˣ = 25
1
,20 - answer-Evaluate (2√5)²
x = -7 or 5 - answer-Solve the quadratic equation by factorisation
x² + 2x - 35 = 0
x = 0 or 4 - answer-Solve the quadratic equation by factorisation
5x² = 20x
49cm² - answer-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 - answer-What is the quadratic formula?
x = -(5/2) - answer-Solve the quadratic equation
(2x² + 5x + 3) / (x² + 3x + 2) = 4
x ≥ 2 - answer-Solve
2x + 7 ≤ 8x - 5
x ≤ 2/5 - answer-Solve
4x - 7(2x - 1) ≥ 3
x ≤ - 1 - answer-Solve
2
,(4 + x) / 3 ≤ 1 - 5(1 + x)
-5 ≤ x ≤ 1/2 - answer-Solve and sketch the inequality
(5 + x)(1 - 2x) ≥ 0
x ≤ -7/2 or x ≥ -4/5 - answer-Solve and sketch the inequality
10x² + 43x + 28 ≥ 0
x ≤ 2, x ≥ 6 - answer-Solve and sketch the inequality
(x² + 12) / 2 ≥ 4x
(x + b/2)² - (b/2)² + c - answer-Complete the square
x² + bx + c
(x - 5)² - 5 - answer-Write in the form (x + p)² + q
x² - 10x + 20
x = 2 ± 2√3 - answer-Complete the square to find x
x² - 4x - 8 = 0
x = 6 ± 0.5√170 - answer-Complete the square to find x
4x² - 48x - 26
x = 0.42 or 1.58 - answer-Solve using the quadratic formula to 2 decimal places.
3
, 3x² = 6x - 2
x = (-5 ± √57) / 4 - answer-Solve using the quadratic formula.
2x² -4 + 5x = 0
(-1 - √5) / 2 < x < (-1 + √5) / 2 - answer-Solve using the quadratic formula.
x² < 1 - x
3 - answer-How many significant figures should your final answer in the exam have?
x = ± 1.79 - answer-Solve using the quadratic formula.
To 3 sig figures.
2x⁸ - 20x⁴ - 7 = 0
x = (-b ± √b² - 4ac) / 2a - answer-Complete the square to find x
ax² + bx + c = 0
(draw the graph) - answer-Show that x² + 8x + 16 ≥ 0 for all values of x
(delta) - answer-What is the symbol for the discriminant?
(delta) = b² - 4ac - answer-What is the equation for the discriminant?
(delta) = -23
There are no real roots - answer-Work out the discriminant and determine how many roots the
4
