National 5 Prelim Revision Topics Worksheet - Elgin Academy Page 2
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2
3
4
5���� = �
���� =
����
3����+5����
a) ℎ = 5����
− 9����
2
2����
����
b)
c)
Brackets
• Expand and simplify expressions with brackets
a) (���� + 8)(3���� − 7)
b) (���� − 7)(����
+ 6���� − 5)
e.g. 10 Expand and simplify:
2
• Factorise expressions
a) 4����
− 9
b) 15����
���� + 35��������
c) ����
− ���� − 30
e.g. 11 Factorise fully:
2
2
3
2
d) 5����
− 80
e) 3����
+ 13���� − 10
2
2
• Create and solve expressions involving brackets
e.g. 12 Two numbers are multiplied together to make 60. If one number is 11 more than
the other number (x), create an equation to represent this situation. Solve this equation to
find two possible values for x.
Quadratics
• Solving by factorising
a) 3����
− 24���� = 0
b) ����
+ 3���� − 40 = 0
c) 25����
− 49 = 0
2
2
2
e.g. 13 Solve:
• Solving using the quadratic equation
Solve 4����
− 5���� − 7 = 0 giving your answers correct to 3 sig figs.
2
e.g. 14
• Finding roots and turning points
a) ���� = (���� − 6)(���� + 4)
b) ���� = 4����(���� − 10)
c) ���� = ����
− 10���� + 9
e.g. 15 Find i) the roots ii) the line of symmetry iii) the turning point for each graph:
2
• Completing the Square
e.g. 16 Write in the form ( ���� + ���� )
+ ����
2
a) ����
+ 10���� − 9
b) ����
− 12���� + 30
2
2
Simultaneous Equations
• Create and solve simultaneous equations
e.g. 17
Three adults and two children pay £68.90 for theatre tickets to see the Lion King. A group
of 2 adults and 3 children pay £59.60 for the same show. Calculate the cost of each ticket.
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