a = 4 and b = -3. Work out the value of each expression.
(a)a + b(1)
(b)ab(2)
(c)a - 2b(2)
(Total for Question 3 is 5 marks)
4
y = -2. Work out the value of each expression.
(a)y2(2)
(b)y3(2)
(c)y2 + 5(2)
(Total for Question 4 is 6 marks)
5
x = -5. Work out the value of each expression.
(a)4(x + 3)(2)
(b)2(5 - x)(2)
(Total for Question 5 is 4 marks)
6
The perimeter of a rectangle is given by P = 2(l + w), where l is the length and w is the width. Work out P when l = 8.5 cm and w = 3.2 cm.
Diagram NOT accurately drawn
(Total for Question 6 is 2 marks)
7
Average speed can be found using speed = distance / time. Work out the average speed for each journey.
(a)A car travels 180 km in 2.5 hours.(2)
(b)A cyclist travels 45 km in 3 hours.(2)
(Total for Question 7 is 4 marks)
8
The area of a trapezium is given by A = 1/2(a + b)h, where a and b are the lengths of the parallel sides and h is the height. Work out the area of a trapezium with a = 6 cm, b = 10 cm and h = 4 cm.
Diagram NOT accurately drawn
(Total for Question 8 is 3 marks)
9
The formula v = u + at gives the final speed of an object, where u is the initial speed, a is the acceleration and t is the time. Work out v for each set of values.
(a)u = 4, a = 9.8 and t = 2.5(2)
(b)u = -3, a = 4 and t = 6(2)
(Total for Question 9 is 4 marks)
10
x = -3 and y = 4. Work out the value of 2x2 + 3y.
(Total for Question 10 is 3 marks)
11
p = -3. Work out the value of each expression.
(a)-p2(2)
(b)(-p)2(2)
(Total for Question 11 is 4 marks)
12
Show that x = 3 is not a solution of the equation 2x2 - 5x = 12.
(Total for Question 12 is 2 marks)
13
A plumber uses the formula C = 45 + 30h to work out the cost, C pounds, of a job, where h is the number of hours worked.
(a)Work out the cost of a job that takes 3.5 hours.(2)
(b)A different job costs 165 pounds. Work out how many hours the plumber worked.(2)
(Total for Question 13 is 4 marks)
14
a = 5 and b = 2. Work out the value of (a2 - b2) / (a - b).
(Total for Question 14 is 3 marks)
15
Kinetic energy is given by KE = 1/2 m v2, where m is the mass in kg and v is the speed in m/s. Work out the kinetic energy of a car of mass 900 kg travelling at 20 m/s. State the units of your answer.
(Total for Question 15 is 4 marks)
16
x = 3 and y = -1. Work out the exact value of √x2 + 3y. Leave your answer in surd form where appropriate.
(Total for Question 16 is 2 marks)
17
x = -2 and y = 1/4. Work out the value of 1/x + 1/y.
(Total for Question 17 is 3 marks)
18
The time period, T seconds, of a pendulum is given by T = 2 x π x √l/g, where l is the length of the pendulum in metres and g = 9.8 m/s2. Work out T when l = 1.2 m. Give your answer correct to 2 decimal places.
(Total for Question 18 is 3 marks)
19
Two taxi companies use these formulas to work out the cost, C pounds, of a journey of m miles. Company A: C = 2.50 + 1.80m. Company B: C = 4 + 1.50m. Sam needs a taxi for a journey of 6 miles. Work out which company is cheaper for Sam's journey, and by how much.
(Total for Question 19 is 4 marks)
20
The formula for converting a temperature from Celsius (C) to Fahrenheit (F) is F = (9/5)C + 32.
(a)Work out F when C = 35.(2)
(b)Use the formula to work out the value of C when F = 68.(3)
(Total for Question 20 is 5 marks)
Mark scheme · 3.13 Substitution
Question 1
(a) B1 10 cao
(a) Answer: 10
(b) B1 12 cao
(b) Answer: 12
(c) M1 3 x 5 (= 15) seen oe
(c) A1 11 cao
(c) Answer: 11
Question 2
(a) B1 3 cao
(a) Answer: 3
(b) M1 5 - (-3) seen oe
(b) A1 8 cao
(b) Answer: 8
(c) M1 4 x (-3) seen oe
(c) A1 -12 cao
(c) Answer: -12
Question 3
(a) B1 1 cao
(a) Answer: 1
(b) M1 4 x (-3) seen oe
(b) A1 -12 cao
(b) Answer: -12
(c) M1 2 x (-3) (= -6) seen oe
(c) A1 10 cao
(c) Answer: 10
Question 4
(a) M1 (-2)2 seen oe
(a) A1 4 cao
(a) Answer: 4
(b) M1 (-2)3 seen oe
(b) A1 -8 cao
(b) Answer: -8
(c) M1 4 seen (ft from y2) oe
(c) A1 9 cao
(c) Answer: 9
Question 5
(a) M1 -5 + 3 (= -2) seen oe
(a) A1 -8 cao
(a) Answer: -8
(b) M1 5 - (-5) (= 10) seen oe
(b) A1 20 cao
(b) Answer: 20
Question 6
M1 8.5 + 3.2 (= 11.7) seen oe
A1 23.4 cm cao (units required)
Answer: 23.4 cm
Question 7
(a) M1 180 / 2.5 oe
(a) A1 72 km/h cao (units required)
(a) Answer: 72 km/h
(b) M1 45 / 3 oe
(b) A1 15 km/h cao (units required)
(b) Answer: 15 km/h
Question 8
M1 6 + 10 (= 16) seen oe
M1 0.5 x 16 x 4 oe
A1 32 cm2 cao (units required)
Answer: 32 cm2
Question 9
(a) M1 9.8 x 2.5 (= 24.5) seen oe
(a) A1 28.5 cao
(a) Answer: 28.5
(b) M1 4 x 6 (= 24) seen oe
(b) A1 21 cao
(b) Answer: 21
Question 10
M1 2 x (-3)2 (= 18) seen oe
M1 3 x 4 (= 12) seen oe
A1 30 cao
Answer: 30
Question 11
(a) M1 p2 = 9 seen oe
(a) A1 -9 cao
(a) Answer: -9
(b) M1 -p = 3 seen oe
(b) A1 9 cao
(b) Answer: 9
Question 12
M1 2 x 32 - 5 x 3 (= 18 - 15) seen oe
A1 cso, 3 stated and compared with 12, with conclusion that x = 3 is not a solution
Answer: x = 3 is not a solution, since 2(3)2 - 5(3) = 3, not 12
Question 13
(a) M1 30 x 3.5 (= 105) seen oe
(a) A1 150 pounds cao
(a) Answer: 150 pounds
(b) M1 165 - 45 (= 120) seen oe
(b) A1 4 hours cao
(b) Answer: 4 hours
Question 14
M1 25 - 4 (= 21) seen oe
M1 5 - 2 (= 3) seen oe
A1 7 cao
Answer: 7
Question 15
M1 202 (= 400) seen oe
M1 0.5 x 900 x 400 oe
A1 180000 cao
B1 J (joules) stated as the units
Answer: 180000 J
Question 16
M1 9 - 3 (= 6) seen oe
A1√6 oe
Answer: √6
Question 17
M1 1 / (-2) (= -0.5) seen oe
M1 1 / (1/4) (= 4) seen oe
A1 3.5 oe (7/2)
Answer: 3.5 (or 7/2)
Question 18
M1 1.2 / 9.8 (= 0.1224...) seen oe
M1 2 x π x √0.1224... oe, full method
A1 awrt 2.20
Answer: T = 2.20 seconds (2 d.p.)
Question 19
M1 2.50 + 1.80 x 6 (= 13.30) oe
M1 4 + 1.50 x 6 (= 13.00) oe
A1 13.30 and 13.00 both correct cao
C1 correct conclusion that Company B is cheaper, by 0.30 pounds (30p)
Answer: Company B is cheaper, by 0.30 pounds (13.00 pounds compared with 13.30 pounds for Company A)