The density of a substance is given by the formula density = mass / volume, where density is measured in g/cm3, mass in grams and volume in cm3. A block of wood has a mass of 45 g and a volume of 9 cm3. Work out the density of the wood.
(Total for Question 15 is 2 marks)
16
The area of a triangle is given by the formula A = 1/2 b h, where b is the base and h is the perpendicular height. Work out the area of a triangle with base b = 9 cm and height h = 6 cm.
(Total for Question 16 is 2 marks)
17
Simple interest is given by the formula I = (P R T) / 100, where P is the amount invested in pounds, R is the rate of interest per year as a percentage, and T is the time in years. Bilal invests P = 250 pounds at a rate of R = 4% per year for T = 3 years. Work out the simple interest Bilal earns.
(Total for Question 17 is 3 marks)
18
P = 2x2 - 3x + 1. Work out the value of P when x = -4, showing your working.
(Total for Question 18 is 3 marks)
19
Priya substitutes x = -2 into the expression x2 + 4x and gets an answer of -12.
(a)Explain the mistake Priya has made.(1)
(b)Work out the correct value of x2 + 4x when x = -2.(2)
(Total for Question 19 is 3 marks)
20
The nth term of a sequence is given by the expression 3n2 - 5. Sam says, 'When n = 4, the value of the expression is greater than 50.' Determine whether Sam is correct. You must show your working.
(Total for Question 20 is 3 marks)
21
The volume of a cuboid is given by V = lwh. A cuboid has length l = 2x, width w = 3 and height h = x - 1.
(a)Show that V = 6x2 - 6x.(2)
(b)Work out the value of V when x = 5.(2)
(Total for Question 21 is 4 marks)
22
p = 16 and q = -3. Work out the exact value of p1/2 + q3.
(Total for Question 22 is 3 marks)
23
The total surface area of a closed cylinder is given by the formula A = 2 x π x r2 + 2 x π x r x h, where r is the radius and h is the height. A cylinder has radius r = 3 cm and total surface area A = 66 π cm2. Work out the value of h.
(Total for Question 23 is 4 marks)
Mark scheme · 3.13D Substitution: Fluency and Exam Drill
Question 1
B1 30 cao
Answer: 30
Question 2
B1 15 cao
Answer: 15
Question 3
B1 -9 cao
Answer: -9
Question 4
B1 4 cao
Answer: 4
Question 5
B1 -1 cao
Answer: -1
Question 6
B1 12 cao
Answer: 12
Question 7
B1 -6 cao
Answer: -6
Question 8
B1 36 cao
Answer: 36
Question 9
B1 9 cao (a common wrong answer is -9, from not squaring the negative sign correctly - this scores B0)
Answer: 9
Question 10
M1 2 x 6 (= 12) seen oe
A1 15 cao
Answer: 15
Question 11
M1 b + c = -1 seen oe
A1 -3 cao
Answer: -3
Question 12
M1 a2 = 36 and c2 = 4 both evaluated oe
A1 32 cao
Answer: 32
Question 13
B1 16 cao (a common wrong answer is -16 - this scores B0)
Answer: 16
Question 14
M1 p + q = 1 seen oe
A1 1 cao
Answer: 1
Question 15
M1 45 / 9 oe seen
A1 5 g/cm3 cao (units required)
Answer: 5 g/cm3
Question 16
M1 0.5 x 9 x 6 oe seen (or 9 x 6 = 54 seen)
A1 27 cm2 cao (units required)
Answer: 27 cm2
Question 17
M1 250 x 4 (= 1000) seen oe
dM1 1000 x 3 / 100 oe, or (250 x 4 x 3) / 100 seen as a full method
A1 30 pounds cao
Answer: 30 pounds
Question 18
M1 2 x (-4)2 (= 32) seen oe
dM1 -3 x (-4) (= 12) seen, correctly signed
A1 45 cao
Answer: 45
Question 19
(a) B1 correct identification of the error, e.g. she has worked out (-2)2 as -4 instead of +4, oe
(a) Answer: Priya has squared -2 incorrectly, getting -4 instead of the correct value of +4
(b) M1 (-2)2 = 4 correctly stated oe
(b) A1 -4 cao
(b) Answer: -4
Question 20
M1 42 (= 16) seen oe
dM1 3 x 16 - 5 oe, full method for the value of the expression
A1 43 cao, with the correct conclusion that Sam is not correct since 43 is less than 50 (ft the conclusion from their value)
Answer: 43; Sam is not correct, since 43 is less than 50