Quadratic Equations: Higher Worksheet With Answer Key Page 2
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1
2Which grade are you…..?
: HIGHER
Quadratic Equations
ANSWERS
1 Expand
2
ü
ü
a) 4(2x – 5)
8x - 20
b) 3x(5 – 2x)
15x - 6x
2 Factorise fully
2
2
ü
ü
ü
a) 20x - 8
4(5x - 2)
b) 12x
– 10x
2x(6x -5)
c) 6x
– 8xy
2x(3x - 4y)
3 Expand and simplify
2
a) (x + 3)(x + 5)
b) (x – 4)(x + 1)
c) (x – 3)
2
2
2
ü
ü
ü
x
+ 8x + 15
x
- 3x - 4
x
- 6x + 9
4 Factorise and solve
2
2
2
a) x
– x – 20 = 0
b) x
– 7x + 6 = 0
c) x
– 16 = 0
ü
ü
ü
(x - 5)(x + 4)=0
(x - 6)(x - 1)=0
(x - 4)(x + 4)=0
ü
ü
ü
x = 5 x = -4
x = 6 x = 1
x = 4 x = -4
5 Expand and simplify
2
a) (3x + 3)(2x – 3)
b) (4x – 5)
2
2
ü
ü
6x
- 3x - 9
16x
- 40x + 25
6 Factorise and solve
2
2
a) 10x
- 3x - 1 = 0
b) 4x
+ 15x – 4 = 0
ü
ü
(2x - 1)(5x + 1)=0
(4x - 1)(x + 4)=0
ü
ü
x = 0.5 x =-0.2
x = 0.25 x = -4
2
2
üü
7
a) Write y = x
– 6x + 28 in completed square form
(x -3)
+ 19
ü
b) State the minimum value of y
19
2
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8 Solve 3x
- 8x + 2 = 0 . Give your answers correct to 2 decimal places.
2.39 , 0.28
9 Solve algebraically
2
a) The simultaneous equations y = 5 – x
and x + y = 3
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x = -1, y = 4 or x = 4 and y = 1
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= 4x + 7
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b
x = -4 x = -
)
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2
10 A rectangle has length 2x – 1 and width 3x – 2. The area of the rectangle is 33cm
.
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Find the length and width of the rectangle
x = 2.93 4.86 cm x 6.79 cm
35 Marks
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