Question 1
Factorise and thus solve the following quadratic equations, finding both values of x:
1(a) x^2+x-56=0
ANSWER: Multiple Answers (Type 2)
Answer: x = -8, x = 7
Workings:
x^2+x-56=0 = (x-7)(x+8)=0
x= -8 or x= 7
Marks = 3
1(b) x^2-4x +4=0
ANSWER: Simple Text Answer
Answer: x = 2
Workings:
x^2-4x +4=0 = (x -2)(x -2)
x = 2
Marks = 3
1(c) x^2+ 12x + 32=0
ANSWER: Multiple Answers (Type 2)
Answer: x=-4, x=-8
Workings:
x^2+ 12x + 32=0 = (x + 4)(x + 8)
x=-4 or x=-8
Marks = 3
1(d) x^2+ 2x - 35=0
ANSWER: Multiple Answers (Type 2)
Answer: x=-7, x=5
Workings:
x^2+ 2x - 35=0 = (x + 7)(x - 5)
x=-7 or x=5
Marks = 3
Question 2
Factorise and thus solve the following quadratic equations, finding both values of x:
2(a) x^2+5x=6
ANSWER: Multiple Answers (Type 2)
Answer: x=-6, x=1
Workings:
x^2+5x-6 = 0
(x+6)(x-1)=0
x=-6 or x=1
Marks = 3
2(b) x^2- 3x=40
ANSWER: Multiple Answers (Type 2)
Answer: x=8, x=-5
Workings:
x^2- 3x - 40 =0
(x - 8)(x + 5)=0
x=8 or x=-5
Marks = 3
2(c) x^2 + 5=6x[/latex]
ANSWER: Multiple Answers (Type 2)
Answer: x=5, x=1
Workings:
x^2 -6x + 5 = 0
(x - 5)(x - 1)
x=5 or x=1
Marks = 3
2(d) x^2+ 3x= 18
ANSWER: Multiple Answers (Type 2)
Answer: x=3, x=-6
Workings:
x^2+ 3x - 18 = 0
(x - 3)(x + 6)
x=3 or x=-6
Marks = 3
Question 3
Factorise and thus solve the following quadratic equations, finding both values of x:
3(a) x^2+ 14x + 48=0
ANSWER: Multiple Answers (Type 1)
x= -8
x=-6
Workings:
x^2+ 14x + 48 = (x + 8)(x + 6)
(x + 8)(x + 6)=0
x=-8
x=-6
Marks = 2
3(b) x^2+ 13x + 42=0
ANSWER: Multiple Answers (Type 1)
x=-7
x=-6
Workings:
x^2+ 13x + 42 = (x + 7)(x + 6)
(x + 7)(x + 6)=0
x=-7
x=-6
Marks = 2
3(c) x^2+ 10x + 16=0
ANSWER: Multiple Answers (Type 1)
x = -2
x=-8
Workings:
x^2+ 10x + 16 = (x + 2)(x + 8)
(x + 2)(x + 8)=0
x=-2
x=-8
Marks = 2
3(d) x^2+ 12x + 32=0
ANSWER: Multiple Answers (Type 1)
Answer:
x= -8
x=-4
Workings:
x^2+ 12x + 32 = (x +8)(x + 4)
(x + 8)(x +4)=0
x= -8
x=-4
Marks = 2
Question 4
Factorise and thus solve the following quadratic equations, finding both values of x:
4(a) x^2- 10x + 24=0
ANSWER: Multiple Answers
x=4
x=6
Workings
x^2- 10x + 24 = (x - 4)(x - 6)
(x - 4)(x - 6)=0
x=4
x=6
Marks = 2
4(b) x^2- 11x + 28=0
ANSWER: Multiple Answers (Type 1)
x= 4
x= 7
Workings:
x^2- 11x + 28 = (x-4)(x-7)
(x-4)(x-7)=0
x= 4
x= 7
Marks = 2
4(c) x^2- 11x + 30=0
ANSWER: Multiple Answers (Type 1)
x= 5
x = 6
Workings:
x^2- 11x + 30 = (x-5)(x-6)
(x-5)(x-6)=0
x= 5
x = 6
Marks = 2
Question 5
Factorise and thus solve the following quadratic equations, finding both values of x:
5(a) x^2+ x - 30=0
ANSWER: Multiple Answers (Type 1)
x=-6
x=5
Workings:
x^2+ x - 30 = (x+6)(x-5)
(x+6)(x-5)=0
x=-6
x=5
Marks = 2
5(b) x^2+ 2x - 35=0
ANSWER: Multiple Answers (Type 1)
x=-7
x=5
Workings:
x^2+ 2x - 35 = (x+7)(x-5)
(x+7)(x-5)=0
x=-7
x=5
Marks = 2
5(c) x^2+ 4x - 5=0
ANSWER: Multiple Answers (Type 1)
x=-5
x=1
Workings:
x^2+ 4x - 5 = (x+5)(x-1)
(x+5)(x-1)=0
x=-5
x=1
Marks = 2
5(d) x^2- x - 2=0
ANSWER: Multiple Answers (Type 1)
x=-1
x=2
Workings:
x^2- x - 2 = (x+1)(x-2)
(x+1)(x-2)=0
x=-1
x=2
Marks = 2
5(e) x^2- 4x - 5=0
ANSWER: Multiple Answers (Type 1)
x=-1
x=5
Workings:
x^2- 4x - 5 = (x+1)(x-5)
(x+1)(x-5)=0
x=-1
x=5
Marks = 2
Question 6
Factorise and thus solve the following quadratic equations, finding both values of x:
6(a) x^2- 3x - 40=0
ANSWER: Multiple Answers (Type 1)
x=-5
x=8
Workings:
x^2- 3x - 40 = (x+5)(x-8)
(x+5)(x-8)=0
x=-5
x=8
Marks = 2
6(b) x^2+ 5x + 4=0
ANSWER: Multiple Answers (Type 1)
x=-4
x=-1
Workings:
x^2+ 5x + 4 = (x+4)(x+1)
(x+4)(x+1)=0
x=-4
x=-1
Marks = 2
6(c) x^2+ 3x - 18=0
ANSWER: Multiple Answers (Type 1)
x=-6
x=3
Workings:
x^2+ 3x - 18 = (x+6)(x-3)
(x+6)(x-3)=0
x=-6
x=3
Marks = 2
6(d) x^2- 6x + 5=0
ANSWER: Multiple Answers (Type 1)
x=1
x=5
Workings:
x^2- 6x + 5 = (x-1)(x-5)
(x-1)(x-5)=0
x=1
x=5
Marks = 2