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Substitution Quiz

Grade 3 • 3N • 10 Questions (33 Marks)

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Substitution — Notes & Worked Examples Show / Hide

Explanation:

Substitution means replacing letters in an algebraic expression or formula with their given numerical values. Always write brackets around any negative number you substitute — especially when squaring: (−3)² = +9, whereas −3² on a calculator gives −9.

Follow the order of operations (BIDMAS): work out Brackets first, then Indices (powers/roots), then Division and Multiplication, and finally Addition and Subtraction. Remember that 3a means 3 × a.

Example 1: Find the value of 4a − 3b when a = 5 and b = −2.

Solution:

Substitute using brackets: 4(5) − 3(−2)
Multiply: 4 × 5 = 20 and −3 × −2 = +6
= 20 + 6 = 26
Answer: 26

Example 2: Given v = u² + 2as, find v when u = −4, a = 3, and s = 5.

Solution:

Substitute: v = (−4)² + 2(3)(5)
Indices first: (−4)² = −4 × −4 = 16
Multiply: 2 × 3 × 5 = 30
Add: v = 16 + 30 = 46  →  Answer: v = 46
Question 1 AQA Nov 2021 2F Q5
[2 marks]
Work out the value of a2 - 4a when a = 10
Answer
Worked Solution & Answer
a2 - 4a = 102 - 4(10) = 100 - 40 = 60 M1 A1
Answer: Answer 60
Question Paper (PDF) • Mark Scheme (PDF)
Question 2 AQA Nov 2022 2F Q8
[2 marks]
Work out the value of 3r + 4t when r = 13 and t = -2
Answer
Worked Solution & Answer
3(13) + 4(-2) = 39 - 8 = 31 M1 A1
Answer: Answer 31
Question Paper (PDF) • Mark Scheme (PDF)
Question 3
[2 marks]
P = 7r + 3q
Work out the value of P when r = 5 and q = -4
Worked Solution & Answer
P = 7(5) + 3(–4) = 35 – 12 = 23 M1 A1
Answer: 23
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 AQA Nov 2021 3H Q20
[3 marks]
ab = 3c
bc = 2
Work out the value of a when c = 8
Answer
Worked Solution & Answer
From bc = 2, b = 2c M1
When c = 8, b = 2 × 8 = 16 M1
From ab = 3c, a = 3bc = 3 × 16 × 8 = 384. A1
Answer: Answer 384
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Jun 2018 1FR Q20
[3 marks]
E = n2 + n + 5
(a) Work out the value of E when n = 3 [1 mark]
E =
(b) Is Ali correct?
You must give a reason for your answer. [2 marks]
Worked Solution & Answer
(a)
3² + 3 + 5 = 17 B1
Answer (a): E = 17
(b)
When n = 4, E = 16 + 4 + 5 = 25 = 5 × 5, not prime M1 A1
Answer (b): No, when n = 4, E = 4² + 4 + 5 = 25 which is not prime
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 AQA Nov 2023 3F Q5
[3 marks]
(a) d = g2 - 2h
Work out the value of d when g = 15 and h = 63
5 (b) Rearrange m = n + k to make n the subject.
(a) d = g2 - 2h
Work out the value of d when g = 15 and h = 63 [2 marks]
d =
(b) Rearrange m = n + k to make n the subject. [1 mark]
n =
Worked Solution & Answer
(a)
d = 152 - 2(63) = 225 - 126 = 99 M1 A1
Answer (a): d = 99
(b)
Subtract k from both sides: n = m - k B1
Answer (b): n = m - k
Question Paper (PDF) • Mark Scheme (PDF)
Question 7
[4 marks]
T = 3x + 4y
(a) Work out the value of T when x = 5 and y = -7 [2 marks]
(b) Work out the value of y when T = 38 and x = 6 [2 marks]
Worked Solution & Answer
(a)
3(5) + 4(–7) = 15 – 28 = –13 M1 A1
Answer (a): –13
(b)
38 = 3(6) + 4y M1
⇒ 38 = 18 + 4y
⇒ 4y = 20
⇒ y = 5 A1
Answer (b): 5
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Specimen 1F Q9
[4 marks]
T = 3c + 7d
(a) Work out the value of T when c = 9 and d = -2 [2 marks]
(b) Work out the value of P when a = -4 and g = 2 [2 marks]
Worked Solution & Answer
(a)
T = 3(9) + 7(–2) = 27 – 14 = 13 M1 A1
Answer (a): 13
(b)
P = 3(–4)² + 2³ = 3(16) + 8 = 48 + 8 = 56 M1 A1
Answer (b): 56
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Jan 2019 1F Q9
[4 marks]
(a) Given h = 6q - 2u, find h when q = 3 and u = -5 (2) (b) Given B = 3m + 2p, find p when B = 2 and m = 5 (2)
(a) Work out the value of h when q = 3 and u = -5 [2 marks]
h =
(b) Work out the value of p when B = 2 and m = 5 [2 marks]
p =
Worked Solution & Answer
(a)
h = 6(3) - 2(-5) = 18 + 10 = 28 M1 A1
Answer (a): h = 28
(b)
2 = 3(5) + 2p M1
⇒ 2p = -13
⇒ p = -6.5 A1
Answer (b): p = -6.5
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[6 marks]
P = 4x + 3y
x = 5
y = -2
(a) Work out the value of P. [2 marks]
(b) Expand 4e(e + 2) [2 marks]
(c) Solve 3(m - 4) = 21 [2 marks]
m =
Worked Solution & Answer
(a)
4(5) + 3(–2) = 20 – 6 = 14 M1 A1
Answer (a): 14
(b)
Multiply out each bracket first, then collect like terms. M1
e.g. 3(t + 2) + 2(t - 1) = 3t + 6 + 2t - 2 = 5t + 4
Answer: 4e2 + 8e A1
Answer (b): 4e2 + 8e
(c)
m – 4 = 7 M1
⇒ m = 11 A1
Answer (c): m = 11
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 33 marks)
Substitution Worksheets Next: Solving linear equations →

Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables