# GCSE Higher - Algebra

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 Author: HLHSMaths ID: 227918 Filename: GCSE Higher - Algebra Updated: 2013-07-30 07:45:35 Tags: GCSE Higher Algebra Folders: Description: GCSE Higher Algebra questions Show Answers:

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1. A sequence starts:
2, 7, 17, ...
The rule for finding the next term is to multiply the previous term by 2 and then add on 3.
Work out the next term.
37
2. The rule for finding the next term in a sequence is to multiply the previous term by 2 and then add on a, where a is an integer.
The first term is 8 and the fourth term is 127.
8, ..., ..., 127
Work out the value of a.
• 2nd term = 16 + a
• 3rd term = 2(16 + a) + a
•                         or
•                 32 + 2a + a
• 4th term = 2(32 + 3a) + a
•                 64 + 7a = 127
• so a = 9
3. Factorise:
a)

b)

c)

d)
a)

b)

c)

d) 10(x + 2y)(x - 2y)
4. Two families go to a pantomime
The Khan family of 2 adults and 3 children pay £69.
The Lewis family of 3 adults and 5 children pay £109.
Work out the cost of an adult ticket and a child ticket.
• 2a + 3c = 69
• 3a + 5c = 109

Adult a = £18 and Child c = £11
5. Solve this inequality
3x + 7 < x + 8
x =
6. Make a the subject of the formula

7. Solve

x = 1.5 or
8. a) Factorise

b) Factorise
a) x(x + 10)

b) (y + 6)(y - 6)
9. Solve

5w + 6 = 9 - w
10. Solve

2.9
11. Katy is using the quadratic formula to solve a quadratic equation.
After correctly substituting the values, she writes:

a) What is the quadratic equation that Katy is trying to solve?
b) Explain why Katy will not be able to find any solutions to the equation.
a)

b) Can't square root a negative number
12. a) Expand and simplify

b) Hence or otherwise, show that
a)

b)

factorise
13. Solve the simultaneous equations:
2x + 5y = 16
4x + 3y = 11

You must show working.
Do not use trial and improvement.
y = 3 and x =
14. Here are the equations of two straight lines:
y = 7x - 6
y = mx + c

a) Write down the value of m if the lines are perpendicular

b) Write down the values of m and if the lines are reflections of each other in the y axis.
a)

b) m = -7 amd c = -6
15. Simplify fully:

16. Solve the equation

2.57 and -0.91
17. x = ∛(12V/π)
18. You are given the identity
Work out the values of a and b
a = -6

b = -26
19. 50cm
20. 251 is a prime number
(i) Write down the value of √251
(ii) Explain how to test that 251 is a prime number
(i) 15.8

(ii) Divide by numbers and reference to answers being whole numbersand/or decimal
21. 4.6, 4.64, 4.65
22. a) Simplify

b) Expand and simplify (x - 3)(x + 5)

c) Rearrange the formula w = 3(2x + y) - 5
to make x the subject
a)

b)

c)
23. Solve the equation
Give your solutions to 2 decimal places.
2.82 and 1.18
24. Andy and Ben both have some marbles.
If Andy gives Ben 15 marbles, they will have an equal number.
If Ben gives Andy 15 marbles, Andy will have four times as many as Ben.
How many marbles does Andy have?
Andy = 65
25. a) Show that

b) p and q are two numbers.
The sum of p and q is 10.
The product of p and q is 18
Work out the value of
• b)
•                   100 - 2 x 18 = 64
26. Solve the simultaneous equations

2x + 3y = 9
3x + 2y = 1

Do not use trial and improvement
x = -3 and y = 5
27. Find the values of a and b such that

a = 5 and b = -7
28. Make x the subject of the formula

w = √(w - y)
29. Simplify

(5x -1)(x -3)
30. Make x the subject of the formula
• y(x -3) = 3x + 4
• yx -3y = 3x + 4
• yx - 3x = 3y + 4
• x(y - 3) = 3y + 4

31. Find the equation of the straight line passing through the point (0,5) which is perpendicular to the line
32. x = 4.8
33. Solve the simultaneous equations

y = x + 2

Do not use trial and improvement
x = 1 and 2/3

y = 3 and 4/3
34. y is directly proportional to the square of x.
When y = 5, x = 4
Find the value of y when x = 8
20
• Graph 1 = D
• Graph 2 = A
• Graph 3 = E
• Graph 4 = C

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