Question 1
LEVEL 4
Expand and simplify (y + 4)(y - 2).
Select the correct answer from the list below:
A: 2y^2 + 2y - 8
B: y^2 + 2y - 4
C: y^2 + 2y - 8
D: y^2 + 2y - 8
CORRECT ANSWER: C: y^2 + 2y - 8
WORKED SOLUTION:
= (y \times y) + (y \times -2) + (4 \times y) + (4 \times -2)
= y^2 - 2y + 4y - 8
= y^2 + 2y - 8
Question 2
LEVEL 4
Which of the following options is the correct outcome from expanding and simplifying (2x + 1)(x - 3)?
A: 2x^2 - 5x - 3
B: 2x^2 + 5x + 3
C: 2x^2 - 2x + 3
D: 2x^2 - 2x + 3
CORRECT ANSWER: A: 2x^2 - 5x - 3
WORKED SOLUTION:
= (2x \times x) + (2x \times -3) + (1 \times x) + (1 \times -3)
= 2x^2 - 6x + x - 3
= 2x^2 - 5x - 3.
Question 3
LEVEL 4
From the list below, choose the correct expansion of (p + 5q)(q - p).
A: -p^2 + 5q^2
B: 5q^2 - 6pq - p^2
C: 5q^2 - 4pq - p^2
D: p^2 + 5q^2 + 4pq
CORRECT ANSWER: C: 5q^2 - 4pq - p^2
WORKED SOLUTION:
= (p \times q) + (p \times -p) + (5q \times q) + (5q \times -p)
= pq - p^2 + 5q^2 - 5pq
= 5q^2 - 4pq - p^2.
Question 4
LEVEL 4
Expand and simplify the following:
(x+5)(x-2)Select the correct answer from the list below:
A: x^3 +3x -10
B: x^2 +3x -10
C: x +3x -10
D: x^3 +3x +10
CORRECT ANSWER: B: x^2 +3x -10
WORKED SOLUTION:
= (x \times x) + (x \times -2) + (x \times 5) + (5 \times -2) = x^2 + 5x - 2x - 10
x^2 +3x -10Question 5
LEVEL 4
Expand and simplify the following:
(2x+1)^2 -(2x+1)Select the correct answer from the list below:
A:4x^2 +2x + 1
B:4x^2 +2x
C: 4x^2 - 2x
D: 4x^2 +2x - 1
CORRECT ANSWER: B:4x^2 +2x
WORKED SOLUTION:
First expand the (2x+1)^2 by multiplying it out as double bracket
(2x+1)(2x+1) = 4x^2 +4x + 1Then collect like terms from the other bracket -(2x+1)
This leaves you with 4x^2 +2x