Number and algebra: Patterns and algebra Teacher: MAS

Chapter 3: Algebra

Test 2 REVISION (Factorising & Applications) SOLUTIONS

Name: ______Marks: ___ /25

FLUENCY
Mark
The highest common factor of 75 and 100 is:
A  5 Factors of 75: 1, 3, 5, 15, 25, 75
B  25 Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
C  50 Common factors = 1, 5, and 25
D  75 Highest Common Factor (HCF) = 25
E  100
Answer is B / 1
2  / When factorised, 24x – 18y equals:
A  24(x – 2y) HCF = 6
B  3(8x – 6y)
C  18(6x – y)
D  6(4x – 3y)
E  None of the above
Answer is D / 1
3  / The highest common factor of 30a2b and 12a3 is:
A  12a HCF = 6a2
B  2a
C  2a2
D  6a2
E  6a3
Answer is D / 1
4  / When factorised, 2x(c + d) – 4y(c + d) equals:
A  (2x – 4y)(c + d) HCF = (c + d)
B  2(x – 2y)(c + d) 2x(c + d) – 4y(c + d) = (c + d)(2x – 4y)
C  2(2x – 4y)(c + d) = (2x – 4y) (c + d)
D  2x – 4y(c + d) Factorise the first bracket, HCF = 2
None of the above = 2(x – 2y)(c + d)
Answer is B / 1
5  / When factorised, 25m2 – 16n2 equals:
A  (5m – n)(5m + n) Difference of two squares, a2 – b2 = (a – b)(a + b)
B  (5m – 4n)(5m + 4n) 25m2 – 16n2 = (5m)2 – (4n)2
C  (m – 4n)(m + 4n) = (5m – 4n)(5m + 4n)
D  (5m + n)(5m + n)
E  (m – 4n)(m – 4n)
Answer is B / 1
6  / When factorised, what does (x + 2)2 – 9 equal?
A  (x + 2)(x – 3) Difference of two squares, a2 – b2 = (a – b)(a + b)
B  (x + 4)(x – 9) = (x + 2)2 – 32
C  (x – 1)(x + 5) = [(x + 2) – 3][(x + 2) + 3]
D  (x – 1)(x + 3) = (x + 2 – 3)(x + 2 + 3)
E  None of the above = (x – 1)(x + 5)
Answer is C / 1
7  / When factorised and simplified, what does equal?
A  3q + 9 Numerator HCF = 4
B  q + 4 4q + 12 = 4(q+3)
C  4 =
D  4q + 4 = 4
E  3q + 4
Answer is C / 1
8  / When factorised, what does 15x – 10xy + 12 – 8y equal?
A  (5x + 6)(2 – 3y) Factorise by grouping
B  (5x + 4)(3 – 2y) = 5x(3 – 2y) + 4(3 – 2y)
C  (3x – 8)(y + 5) = (3 – 2y)(5x + 4)
D  (2x – 4)(5y – 3) = (5x + 4)(3 – 2y)
E  None of the above
Answer is B / 1
UNDERSTANDING
9  / Factorise 45x2 – 18x.
Answer:
Highest Common Factor = 9x
45x2 – 18x = 9x(5x – 2) / 2
10  / Factorise 5a2b3 + 15a3b2 – 25ab2.
Answer:
Highest Common Factor = 5ab
5a2b3 + 15a3b2 – 25ab2 = 5ab2(ab + 3a2 – 5) / 3
11  / Factorise −56mn + 104m + 42n – 78
Answer:
Factorise by grouping
– 8m(7n – 13) + 6(7n – 13)
= (7n – 13)(– 8m + 6)
(7n – 13)(6 – 8m) or – (7n – 13)(8m – 6) / 4
12  / Factorise each of the following.
(a)  36 – y2
(b)  4x2 – 24x + 9
Answer:
(a)  Difference of two squares, a2 – b2 = (a – b)(a + b)
= 62 – y2
= (6 – y)(6 + y)
(b)  Perfect square, (a ± b)2 = a2 ± 2ab + b2
= (2x)2 – 2 × 2x × 3 + (3)2
= (2x – 3)2 / 4
REASONING
13  / Jackie is making her own cards. She is using a rectangular piece of paper with dimensions 12 cm high and 9 cm wide. She has put p cm margins on the top and bottom of the paper and margins of q cm on the left and right sides of the paper.
(a)  Write an expression for the height of the paper on which he is able to write.
(b)  Write an expression for the width of the paper on which he can write.
(c)  Write an expression for the area of the paper inside the margins.
(d)  If , what is the area allowed for writing?
9 cm

p

12 cm q q

p

Answers:
(a)  cm
[1 mark]
(b) 
[1 mark]
(c) 
[1 mark]
(d) 

[1 mark] / 4

4