AS 91027
Aiming for Achievement
Worksheets
1.2 Apply algebraic procedures in solving problems
4 credits
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AS91027 Apply Algebraic Procedures in Solving Problems
Aiming for Achievement Worksheets
© Kim Freeman
© Mahobe Resources (NZ) Ltd
www.mahobe.co.nz
ISBN(13) 9781877489297
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NCEA Level 1 - Algebra Worksheet 1
Practice Substitution
If a = 4 and b = 5
1. a + 8 = 2. 3b = 3. 2a + 9 = 4. a
2
+ a
2
=
5. 30 ÷ b = 6. 2b + 3 = 7. a
2
+ b = 8. 24 – 4b =
9. a + b = 10. 5a – 2b = 11. 2b – a = 12. 2(a + b) =
13. a + b
2
=
14. 10a – 2b
2
=
15. b
2
– a
2
= 16. 3(2a + 2b) =
17. 5a
2
+ 2b
2
=
18. 8b
2
(a – 2)
=
19. 2.5(a
2
-2b) = 20. 2b(1.5a + 2b) =
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NCEA Level 1 - Algebra Worksheet 2
Substitution Word Problems
Ordering Takeaways Fish is $5.50 per piece
Chips are $3 per scoop
1. What is the cost of 2 pieces of fish?
2. What is the cost of one scoop of chips and 1 piece of fish?
3. What is the cost of 2 fish and 2 scoops of chips?
4. What is the cost of 4 fish and 3 scoops of chips?
5. What did I buy if I spent $14?
6. What did I buy if I spent $28?
7. If I spent $11.50 what could I buy?
8. 14 people order hamburgers. The very hungry ones order 2 each while the rest order 1 each.
They purchase a total of 20 hamburgers. How many people were very hungry?
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NCEA Level 1 - Algebra Worksheet 3
Practice More Substitution
If a = 5, b = 3 and c = -2 calculate:
1. 5a = 2. c + c
2
= 3. 2a + b = 4. 4(a + c) =
5. 2(b – c) = 6. 3a + 4c = 7. -2a + -2c = 8. b
2
– 6a =
9. 10a – 2b = 10. 2(4a + b
2
) = 11.
c
ba
12.
2
4
b
a
13.
c
)8(2
14.
22
)2( cb
15.
)(5.0
2
ba
c
16.
10
abc
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NCEA Level 1 - Algebra Worksheet 4
Collecting Like Terms
Simplify:
1. 5x + 3y – 2x + 9y = 2. 5m
2
+ 3n + 2m
2
– 2n =
3. 3p
3
– 5q
2
+ 9p
3
– 8q
2
= 4. -3x
2
+ 4x + 12x
2
– 12x =
5. Find the total length of all the edges of this cuboid.
Simplify:
6. 14a
2
– 10b – a
2
+ 5b = 7. 22xyz + 12xy – 5xyz + 4x =
8. 8pq + 7p + q + 10pq – q – p = 9. 13x
2
+ 4x
2
– 5y
2
+ y
2
– 12x
2
=
10. 11ab + 2cd – ab + 3dc + ba = 11. 4x – 5x + 3x – x + 2x – 7y =
12. Which is larger and by how much? -13 + 8 – 4 + 6 – 3 + 9
or -31 + 27 – 3 – 6 + 18
3
x
4y
2x
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NCEA Level 1 - Algebra Worksheet 5
Multiplying Algebraic Terms
1. 2x × 6 = 2. -4x × 3y = 3. -3x × -2y =
4. 4y × y = 5. 4 × t × t × t = 6. x
5
× x
5
=
7. 3m
2
× 5m
3
= 8. 2q
2
× 3q
4
× 2q = 9. (6x
2
)
2
=
10. –(3c)
2
= 11. (2a
2
)
3
= 12. (7y
12
)
0
=
Dividing Algebraic Terms
1.
x
15
25
4
= 2. 16x
12
÷ 12x
6
= 3.
10
6
6
9
y
y
=
4.
55
43
yx
yx
= 5.
2
42
5
10
xy
yx
= 6.
3
32
15
30
xy
yx
=
7.
yx
yx
3
24
9
27
= 8.
23
44
yy
yy
= 9.
3
32
4
4
xy
yx
=
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NCEA Level 1 - Algebra Worksheet 6
Brackets, Powers and Roots
Simplify:
1. (x
2
)
3
= 2. (y
2
)
4
= 3. (8a
2
)
2
= 4. (x
2
y
5
)
2
=
5. (2x
3
y
2
)
5
= 6. (5a
2
b)
4
= 7.
2
3
2
y
x
= 8.
4
2
3
y
x
=
9.
3
4
2
2
x
x
= 10.
2
2
x
x
= 11.
7
5
x
x
= 12. (12x
2
)
0
=
13. 5x
0
= 14.
3
4
8
2
x
x
15.
2
22
5
52
x
xx
16.
2
5
2
x
x
17.
3
2
4xx
18.
16
9x
= 19.
64
64x
= 20.
3
12
64x
=
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NCEA Level 1 - Algebra Worksheet 7
Order of Operations
Simplify
1. 3y + y × y 2. 5 × (a + a) × a 3. 6x + 3x ÷ x
4. 3y – 3y × 2y 5. 10y + 8y ÷ y 6. 2z + (2z)
2
× 2z
7.
x
xx
2
3
8.
x
x
xx
7
5
46
9.
yy
yy
58
54
22
10. 10x ÷ 2 + 4x 11. y + y ÷ y – y 12.
22
2
)(
yy
yyy
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NCEA Level 1 - Algebra Worksheet 8
Simplifying Fractions
Simplify:
1.
3
24x
2.
2
15y
3.
2
12
16
x
4.
3
9
y
y
5.
8
10
8
x
x
6.
10
85
6
xy
yx
7.
4
8
5
25
z
z
8.
10
6
4
8
x
x
9.
108
510
6
9
yx
yx
10.
3
2
3
2
4
x
x
11.
2
3
2
4
2
xy
xy
12.
2
33
)2(
4
xy
yx
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NCEA Level 1 - Algebra Worksheet 9
Algebraic Fractions
Simplify:
1.
9
3
9
5 xx
2.
15
6
15
8 xx
3.
y
x
y
x3
4.
2
4
xx
5.
5
2
4
3
32
xx
6.
4
5
3
1 xx
7.
3
2
5
4 yy
8.
2
3
5
2
x
x
9.
5
3
2 xx
10.
x
x
3
1
5
11.
21
2
9
3
24
xx
12.
z
z
xy 2
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NCEA Level 1 - Algebra Worksheet 10
Expanding (1)
Expand these expressions:
1. 4(2x + y) 2. 5(5x – 2) 3. y(y + 2)
4. x(2x + 5) 5. 2y(3y – 8) 6. -3(x – 2)
Expand and simplify these expressions:
7. 3(x + 1) + 2(x + 3) 8. 4x + 3(x + 5) 9. 6(x – 2) + 2(2x – 1)
10. -2(y + 3) + 5(2y – 1) 11. 5(x + 8) – 4(x – 5) 12. 5(z – 1) – 2(z + 4)
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NCEA Level 1 - Algebra Worksheet 11
Expanding (2)
Expand these expressions:
1. 4(2x + y) 2. 5(5x – 2) 3. y(y + 2)
4. x(2x + 5) 5. 2y(3y – 8) 6. -3(x – 2)
Expand and simplify these expressions:
7. 3(x + 1) + 2(x + 3) 8. 4x + 3(x + 5) 9. 6(x – 2) + 2(2x – 1)
10. 2(y + 3) - 5(2y – 1) 11. -5(x + 8) + 4(x + 5) 12. 5(z + 1) – 2(z + 4)
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NCEA Level 1 - Algebra Worksheet 12
Expanding (3)
Expand these brackets:
1. (x + 4)(x + 6) 2. (x + 4)(x – 5) 3. (y – 6)(y – 3)
4. (x – 2)(x + 15) 5. (2y + 5)(y + 2) 6. (4x – 5)(3x + 2)
7. (4y – 2)(3y – 5) 8. (2x + y)(x + y) 9. 8 + 5x(x – 9)
10. (x + 6)
2
11. (2x + 5)
2
12. (5 – 2y)(5 + 2y)
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NCEA Level 1 - Algebra Worksheet 13
Factorising (1)
Factorise:
1. 5x + 5y 2. 12x + 3y 3. 20g – 10h
4. 12s – 16t 5. 30 – 16x 6. 4xy
2
+ 8xy
7. 5g + gh 8. xy + 10y 9. 3xy + 5y
10. 3pq – q
2
11. 8xy + 24x 12. 3x
2
y – x
3
13. 2xy
2
+ 4x
2
y 14. 6a
2
b
2
+ 3ab 15. 12ab + 14
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NCEA Level 1 - Algebra Worksheet 14
Factorising (2)
Factorise:
1. x
2
+ 10x + 21 2. x
2
– 2x + 1 3. x
2
– x – 20
4. x
2
– 2x – 15 5. x
2
+ 4x – 45 6. x
2
+ 21x – 100
7. x
2
– 8x – 20 8. x
2
+ 8x + 15 9. x
2
+ 3x – 40
10. x
2
– 36 11. 4x
2
– 16 12. x
2
+ 14x + 49
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NCEA Level 1 - Algebra Worksheet 15
Harder Factorising
Factorise:
1. x
2
– 21 = 4x 2. x
2
= 25x 3. x
2
– 300 = 20x
4. 2x
2
+ 14x + 12 5. 2x
2
+ 16x + 24 6. 3x
2
+ 15x + 18
7. 3x
2
+ 3x – 60 8. 5x
2
– 5x – 30 9. x + 1 =
x
12
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NCEA Level 1 - Algebra Worksheet 16
Solving Equations (1)
Solve for x:
1. 4x + 2 = 34 2. 3x + 4 = 25 3. 8y – 5 = 35
4.
7
x
= 5 5.
4
x
+ 9 = 16 6.
3
2
x
= 7
7.
2
42
x
= 8 8. 2(x + 10) + 6 = 50 9. 3x + 25 = 8x – 10
10.
2
64
x
+ 5 = 18 11. 8x – 16 = 6x + 2 12. 12 – x = 9x
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NCEA Level 1 - Algebra Worksheet 17
Solving Equations (2)
Solve these equations:
1. x – 10 = 3(x + 2) 2. -4(x + 5) = 16
3. 5(x + 5) = 3(x – 4) 4. 3(x – 3) – (x – 2) = 5
5. 10(x + 3) – 4(x – 2) = 7(x + 5) 6.
2
x
= 48
7.
x
120
= 16 8. 30 –
2
x
= 28
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NCEA Level 1 - Algebra Worksheet 18
Solving Equations (3)
Solve these equations:
1.
5
4
3
6
xx
2.
3
7
4
12
xx
3.
4
3
12
x
4.
11
5
1
x
5.
x
x
12
4
6.
10
3
4
3
xx
7.
5
5
113
3
xx
8.
0
2
7
43
xx
9.
0
2
12
4
36
xx
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NCEA Level 1 - Algebra Worksheet 19
Quadratic Graphs
Complete the tables and plot points:
1. y = x
2
– 3 2. y = x
2
+ 2x 3. y = (x – 1)(x + 1)
x y
-3
-2
-1
0
1
2
3
x y
-3
-2
-1
0
1
2
3
y
x
1 2 3 4 5 – 1 – 2 – 3 – 4 – 5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
– 1
– 2
– 3
– 4
x y
-3
-2
-1
0
1
2
3
y
x
1 2 3 4 5 – 1 – 2 – 3 – 4 – 5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
– 1
– 2
– 3
– 4
y
x
1 2 3 4 5 – 1 – 2 – 3 – 4 – 5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
– 1
– 2
– 3
– 4
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NCEA Level 1 - Algebra Worksheet 20
Solving Quadratics
Solve:
1. x
2
+ 8x + 12 = 0 2. x
2
– 4x + 3 = 0 3. x
2
+ 11x – 26 = 0
4. x
2
– 2x – 120 = 0 5. x
2
– 81 = 0 6. x
2
+ 4x = 45
7. x
2
+ 36 = 13x 8. x(x – 3) = 10 9. (x + 2)
2
= 9
10. x
2
– 2x = 15 11. x
2
– 20 = x 12. x
2
= 11x
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NCEA Level 1 - Algebra Worksheet 21
Solving Quadratic Word Problems
1. A rectangular swimming pool has an area of 54m
2
.
The width of the pool is x metres and the difference between the length and the width is 3 metres.
What is the width of the pool.
2. A triangle has a base of 2x cm and a height of (x + 1) cm. If the area of the triangle is 20 cm
2
calculate the value of x.
3. Kate is 10 years old, and James is 8 years old.
In how many years will the product of their ages be 143?
4. When a number, x, is squared, and then 15 is subtracted the result is 34.
What is the value of x.
5. Squaring a number, x, and then adding 2 times the original number gives a result of 24.
Write this problems as a quadratic equation then solve to find the value ot x.
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NCEA Level 1 - Algebra Worksheet 22
Solving Exponents
Solve for x:
1. x
3
= 216 2. x
4
= 81 3. x
5
= 1024
4. x
3
+ 10 = 74 5. x
3
– 20 = 105 6. 3x
6
= 192
7. 6x
3
= 750 8. 2x
4
+ 512 = 1024 9.
54
4
3
x
10. 2
x
= 256 11. 6
x
= 1296 12. 5
x
+ 75 = 200
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NCEA Level 1 - Algebra Worksheet 23
Simultaneous Equations
Solve for x and y:
1. 5x + 2y = 34 2. 3x + 2y = 56 3. 3x = y
4x – 2y = 2 2x + 2y = 44 x – y = -4
4. 4x + 6y = 16 5. 3x + 2y = 26.5 6. 4x = y
x + 2y = 5 x = y – 4.5 100x – 10y = 315
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NCEA Level 1 - Algebra Worksheet 24
Simultaneous Equation Word Problems
1. Two farmers are buying livestock at the sales. Farmer Janis buys 6 calves and 5 lambs for $860.
Farmer Fred buys 4 calves and 10 lambs for $1000. By writing this problem as a pair of
simultaneous equations calculate the cost of the calves and lambs.
2. You spend $335 on 340 square tiles for your bathroom floor. You buy x small tiles at 80 cents each
and y big tiles for $1.50 each. Form a pair of simultaneous equations and calculate the number of
big and small titles that you purchased.
3. An equilateral triangle has sides (6x – y) cm, (5x + 5) cm and (2x + 5y) cm long.
The perimeter of the triangle is 240 cm. Write down 2 equations connecting x and y and then solve
to find the value of x and y.
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NCEA Level 1 - Algebra Worksheet 25
Inequalities
Solve:
1. 8x < 24 2. y + 6 ≥ 15 3. 3x + 5 ≤ 39
4. 22 + x > 30 5. x – 5 ≥ 24 6. 4y + 2 ≤ 2y + 11
7. -10x < 30 8. -5y ≥ -25 9. 32 – 4x ≤ 40
Mark the values on the number lines:
10. -4 < x ≤ 2 x
R 11. -2 ≤ x ≤ 2 x
R
12 -3 < x < 2 x
I 13. -2 < x ≤ 3 x
I
-
4
-
3
-
2
-
1
0
1
2
3
-
4
-
3
-
2
-
1
0
1
2
3
-4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3
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NCEA Level 1 - Algebra Worksheet 26
Factorising and Fractions
Simplify:
1.
38
x
2.
x
xx
3
96
3.
55
25
xx
x
4.
52
210
xx
xx
5.
x
xx
3
126
2
6.
x
x
x
3
2
3
7.
3
2
128
2
xx
8.
12
2410
2
2
xx
9.
15
8
124
2
x
x
x
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NCEA Level 1 - Algebra Worksheet 27
Rearranging Formulas
Rearrange the formulas to make the letter in brackets the new subject.
1.
10
3y
x
2.
ba 510
3.
)10(
2
1
xd
(y) (b) (x)
4.
)3(2 mk
5.
3
2y
x
6.
20
6
2
t
s
(m) (y) (t)
7.
2
4yx
8.
10
2
xy
9.
2
2
p
q
(y) (x) (p)
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NCEA Level 1 - Algebra Worksheet 28
6
5
24
x
37
2
5
x
2
5
3
2
x
164
2
3
x
14)1(2
x
11
2
28
x
4
3
6
5
x
61
2
5
x
147)9(7
x
4
5
22
x
Algebra Revision I
Solve:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 6x + 3 = 2x + 13
12. 13x – 5 = x – 29
13. 6x – 40 = 2x
14. 3x + 8 = x + 1
15. 10x + 30x = 100
16. 2x + 12 = 5x – 3
17. 3x – 8 = 4x – 7
18. 15x – 23 = 10x + 18
19. 7x – 5 = 5x + 45
20. 4x – 20x = 36
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NCEA Level 1 - Algebra Worksheet 29
Solve
21. 4x(x – 5) = 0
22. 2x(x + 8) = 0
23. (x + 2)(x – 2) = 0
24. (x – 6)(2x – 4) = 0
25. (x + 5)(5x – 4) = 0
26. (2x + 9)(x – 5) = 0
27. 10x(x + 5) = 0
28. (x + 8)(4x + 1) = 0
29. (x + 7)(2x + 7) = 0
30. (2x + 1)(x – 2) = 0
Expand
31. (x + 8)(x + 9)
32. (x – 10)(x + 15)
33. (x + 7)(x – 3)
34. (x – 8)(x – 5)
35. (x + 6)(x – 6)
36. (x + 7)
2
37. (x – 10)
2
38. (2x + 5)(x + 2)
39. (3x + 1)(x – 7)
40. (2x – 9)(x + 4)
Mahobe Resources (NZ) Ltd
NCEA Level 1 - Algebra Worksheet 30
x
x
15
9
2
2
5
4
12
x
x
20
12
15
18
x
x
3
2
6
x
x
Algebra Revision II
Simplify:
1.
2.
3.
4.
5. 3x
2
× 2x
3
6. 12y
5
× 2y
4
7. 6x × 6x × 2x
2
8. 3(x – 5) + 2(x – 2)
9. 6(x – 4) + 2(2x + 1)
10. 3x – 8(x + 1)
Factorise
11. x
2
+ 3x – 28
12. x
2
+ 10x + 16
13. x
2
– 6 – 40
14. x
2
– 20x + 75
15. x
2
+ 16x + 64
16. x
2
– 4x + 4
17. 2x
2
– 4x – 48
18. 2x
2
+ 22x + 56
19. x
2
– 20x – 125
20. x
2
+ 100x + 2400
Mahobe Resources (NZ) Ltd
NCEA Level 1 - Algebra Worksheet 31
y
xz
7
4
20
x
x
x
9
)3(
32
If x = 5, y = -2.5 and z = 4 find:
21. 2x + 5
22. 2x
2
+ 4y
23. 0.8(2x + 5z)
24. y
2
+ z
25.
26. 8xy + 4z
27. -2x + -2y + -2z
28. -6 × (2x – 2y)
2
29. x(z
2
+ 2y)
30. -6x + (-6yz)
Find the rule for these patterns.
31. x 1 2 3 4 5
y 7 9 11 13 15
32. x 1 2 3 4 5
y 0 _ 6 9 12
33. x 1 2 3 4 5
y _ -9 _ -19 -24
34. x 1 2 3 4 5
y 3.5 _ 5.5 _ 7.5
35. Solve 5(x + 4) = 10
36. Solve 4x + 2 = 2x + 1
37. Factorise 3x
2
+ 6x + 3
38. Solve
39. Simplify
40. Solve (x
2
)
4
= 256
Mahobe Resources (NZ) Ltd
NCEA Level 1 - Algebra Worksheet 32
2
65
2
x
xx
4
32
.2
y
yy
3
5
12
9
x
x
5
2
8
2
x
x
Algebra Revision III
Expand and Simplify:
1. 3(x + 1) + 2(x – 4)
2. (3x – 1)(2x + 4)
3. (2x – 1) + (x – 4)
4. (x – 3)
2
5. 2(x + 2) – 3(x – 4)
6. (5y + 2)(y + 4)
Solve:
7. x
2
– 7x + 6 = 0
8. 5x
2
– 20x = 0
9. 2x
2
– 4x – 16 = 0
10. 4x
2
– 9 = 0
11. x
2
– 5x – 24 = 0
12. x
2
+ 8x – 20 = 0
Simplify:
13. 3x
4
× 2x
3
14.
15.
16.
17. (2x
2
)
4
18.
19. (x + 50) is a factor of:
x
2
+ 10x – 2000
What is the other factor?
20. 5(x
2
)
n
× 3x
4
= 15x
12
What is the value of n?
Mahobe Resources (NZ) Ltd
NCEA Level 1 - Algebra Worksheet 33
2
2
3
153
x
xyx
5
2
3
xx
2
5
3
2 xx
21. Zeba is estimating the area and circumference of a circle by
using π = 3. She uses the formulas A = 3r
2
and C = 6r.
What would the area and circumference of a circle be if the
radius was 7.5 cm?
22. In a diving competition the judges calculate the score (S) by
using the formula S = 0.8DT where D is the degree of difficulty
and T is the total of all the judges marks.
Alyssa does a dive with a difficulty degree of 2.5.
The total of the judges marks was 36.5
Calculate the score for Alyssa’s dive.
23. Last December Levar’s parents opened a savings account for
his university study. They made an initial deposit (x) and have
added $150 each month since. At the end of August there was
$1775 in the account. Below is a diagram of the deposits.
Dec →Jan→ Feb→ Mar→ Apr→ May→ Jun→ July→ Aug
x →
+
150 →
+
150 →
+
150 →
+
150 →
+
150 →
+
150 →
+
150→
+
150
Write an expression for the amount of money that has been put
into the account and use it to calculate the initial deposit (x).
Simplify:
24. 25. 26.
Mahobe Resources (NZ) Ltd
6
4
y
x
8
12
y
x
6
8
x
2
1
x
3
5
3
x
3
4
6
x
4
2
3
y
yx
2
1
3
2
Answers
Worksheet 1
Practice Substitution
1. 12
2. 15
3. 17
4. 32
5. 6
6. 13
7. 21
8. 4
9. 9
10. 10
11. 6
12. 18
13. 29
14. -10
15. 9
16. 54
17. 130
18. 400
19. 15
20. 160
Worksheet 2
Substitution Word Problems
1. $11
2. $8.50
3. $17
4. $31
5. 2 fish, 1 chips
6. 4 fish, 2 chips
7. 1 fish, 2 chips
8. 6 very hungry
Worksheet 3
Practice More Substitution
1. 25
2. 2
3. 13
4. 12
5. 10
6. 7
7. -6
8. -21
9. 44
10. 58
11. -4
12. 1
13. 2
14. ±5
15. 1
16. 3
Worksheet 4
Collecting Like Terms
1. 3x + 12y
2. 7m
2
+ n
3. 12p
3
– 13q
2
4. 9x
2
– 8x
5. 16y + 20x
6. 13a
2
– 5b
7. 17xyz + 12xy + 4x
8. 18pq + 6p
9. 5x
2
– 4y
2
10. 11ab + 5cd
Note cd = dc
11. 3x – 7y
12. First sum = 3
Second sum = 5
Second larger by 2
Worksheet 5
Multiplying Algebraic Terms
1. 12x
2. -12xy
3. 6xy
4. 4y
2
5. 4t
3
6. x
10
7. 15m
5
8. 12q
7
9. 36x
4
10. -9c
2
11. 8a
6
12. 1
Dividing Algebraic Terms
1.
2.
3.
4.
5. 2xy
2
6. 2x
7. 3xy
8. y
3
9. x
Worksheet 6
Brackets, Powers and Roots
1. x
6
2. y
8
3. 64a
4
4. x
4
y
10
5. 32x
15
y
10
6. 625a
8
b
4
7.
8.
9.
10. 1
11.
12. 1
13. 5
14. 2x
15. 2x
2
16. 4x
9
17. 64x
7
18. 3x
8
19. 8x
32
20. 4x
4
Worksheet 7
Simplifying Fractions
1. 3y + y
2
2. 10a
2
3. 6x + 3
4. 3y – 6y
2
5. 10y + 8
6. 2z + 8z
3
7. 2
8. -5
9. 3y
10. 9x
11. 1
12.
Mahobe Resources (NZ) Ltd
2
3
4
x
2
4
6
y
x
4
2
x
5
2
2
3
y
x
9
8x
15
2x
y
x4
4
3x
5
23
32
xx
12
11
x
15
8
2
y
x
5
6
15
2
2
x
5
3
2
x
2
7
2
x
2
xy
Worksheet 8
Simplifying Fractions
1. 8x
2. 7.5y,
3.
4. y
6
5. 8x
2
6.
7. 5z
4
8.
9.
10. 8x
3
11. 2x
2
y
4
12. xy
Worksheet 9
Algebraic Fractions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12.
Worksheet 10
Expanding (1)
1. 8x + 4y
2. 25x – 10
3. y
2
+ 2y
4. 2x
2
+ 5x
5. 6y
2
– 16y
6. -3x + 6
7. 5x + 9
8. 7x + 15
9. 10x – 14
10. 8y – 11
11. x + 60
12. 3z – 13
Worksheet 11
Expanding (2)
1. 8x + 4y
2. 25x – 10
3. y
2
+ 2y
4. 2x
2
+ 5x
5. 6y
2
– 16y
6. -3x + 6
7. 5x + 9
8. 7x + 15
9. 10x – 14
10. -8y + 11
11. -x – 20
12. 3z – 3
Worksheet 12
Expanding (3)
1. x
2
+ 10x + 24
2. x
2
– x – 20
3. y
2
– 9x + 18
4. x
2
+ 13x – 30
5. 2y
2
+ 9y + 10
6. 12x – 7x – 10
7. 12y
2
– 26y + 10
8. 2x
2
+ 3xy + y
2
9. 8 + 5x
2
– 45x
10. x
2
+ 12x + 36
11. 4x
2
+ 20x + 25
12. 25 – 4y
2
Worksheet 13
Factorising (1)
1. 5(x + y)
2. 3(4x + y)
3. 10(2g – h)
4. 4(3s – 4t)
5. 2(15 – 8x)
6. 4xy(y + 8)
7. g(5 + h)
8. y(x + 10)
9. y(3x + 5)
10. q(3p – q)
11. 8x(y + 3)
12. x
2
(3y – x)
13. 2xy(y + 2x)
14. 3ab(2ab + 1)
15. 2(6ab + 7)
Worksheet 14
Factorising (2)
1. (x + 7)(x + 3)
2. (x – 1)
2
3. (x – 5)(x + 4)
4. (x – 5)(x + 3)
5. (x + 9)(x – 5)
6. (x + 25)(x – 4)
7. (x – 10)(x + 2)
8. (x + 5)(x + 3)
9. (x + 9)(x – 5)
10. (x + 6)(x – 6)
11. (2x – 4)(2x + 4)
12. (x + 7)
2
Worksheet 15
Harder Factorising
1. (x – 7)(x + 3)
2. x(x – 25)
3. (x – 30)(x + 10)
4. 2(x + 6)(x + 1)
5. 2(x + 6)(x + 2)
6. 3(x + 3)(x + 2)
7. 3(x + 5)(x – 4)
8. 5(x – 3)(x + 2)
9. (x + 4)(x – 3)
Worksheet 16
Solving Equations
1. x = 8
2. x = 7
3. y = 5
4. x = 35
5. x = 28
6. x = 19
7. x = 10
8. x = 12
9. x = 7
10. x = 5
11. x = 9
12. x = 1.2
Mahobe Resources (NZ) Ltd
5
5
x
5
10
x
x
3
2
2
x
x
3
6
x
x
5
4
x
3
10x
y
5
10 a
b
2
6
k
m
2
3x
y
12016 st
4
x
t
10 yx
qp 2
Worksheet 17
Solving Equations (1)
1. x = -8
2. x = -9
3. x = -18.5
4. x = 6
5. x = 3
6. x = 12
7. x = 7.5
8. x = ±2
Worksheet 18
Solving Equations (2)
1. x = -9
2. x = -15.5
3. x = 9
4. x = 54
5. x = 16
6. x = 24
7. x = 3
8. x = 8
9. x = 2.5
Worksheet 19
Quadratic Graphs
1. y = 6, 1, -2, -3, -2, 6
2. y = 3, 0, -1, 0, 3, 8, 15
3. y = 8, 3, 0, -1, 0, 3, 8
See your teacher and have
them check your graphs
for accuracy.
Worksheet 20
Solving Quadratics
1. x = -6, -2
2. x = 3, 1
3. x = -13, 2
4. x = 12, -10
5. x = ±9
6. x = -9, 5
7. x = 9, 4
8. x = 5, -2
9. x = -5, 1
10. x = 5, -3
11. x = 5, -4
12. x = 0, 11
Worksheet 21
Quadratic Word Problems
1. x = 6
2. x = 4
3. x = 3
4. x = ±7
5. x = -6 or x = 4
Worksheet 22
Solving Exponents
1. x = 6
2. x = 3
3. x = 4
4. x = 4
5. x = 5
6. x = 2
7. x = 5
8. x = 4
9. x = -6
10. x = 8
11. x = 4
12. x = 3
Worksheet 23
Simultaneous Equations
1. x = 4, y = 7
2. x = 12, y = 10
3. x = 2, y = 6
4. x = 1, y = 2
5. x = 3.5, y = 8
6. x = 5.25, y = 21
Worksheet 24
Word Problems
1. 90 calves, 64 lambs
2. Small (x) = 250
Large (y) = 90
3. y = 10, x = 15
Worksheet 25, Inequalities
1. x < 3
2. y ≥ 9
3. x ≤ 11.33
4. x > 8
5. x ≥ 29
6. y ≤ 4.5
7. x > -3
8. y ≤ 5
9. x ≥ -2
10. Have your teacher check
numbers 10 – 13.
Worksheet 26
Factorising and Fractions
1. 4x + 12
2. 2x – 3
3.
4.
5. 2x + 4
6.
7. 4x
8.
9.
Worksheet 27
Rearranging Formulas
1.
2.
3. x = 2d – 10
4.
5.
6.
7.
8.
9.
Mahobe Resources (NZ) Ltd
2
3
x
8
5
6
x
4
3
2
x
3
4
1
x
15
11x
6
19x
5
3x
Worksheet 28
Algebra Revision I
1. x = 7
2. x = 4
3. x = 3.75
4. x = 8
5. x = 8
6. x = 3
7. x = 0.9 (9/10)
8. x = 2
9. x = 12
10. x = 9
11. x = 2.5
12. x = -2
13. x = 10
14. x = -3.5
15. x = 2.5
16. x = 5
17. x = -1
18. x = 8.2
19. x = 25
20. x = -2.25
Worksheet 29
21. x = 0, 5
22. x = 0, -8
23. x = ±2
24. x = 6, 2
25. x = -5, 4/5
26. x = -4.5, 5
27. x = 0, -5
28. x = -8, -1.25
29. x = -7, -3.5
30. x = -0.5, 2
31. x
2
+ 17x + 72
32. x
2
+ 5x – 150
33. x
2
+ 4x – 21
34. x
2
– 13x + 40
35. x
2
– 36
36. x
2
+ 14x + 49
37. x
2
– 20x + 100
38. 2x
2
+ 9x + 10
39. 3x
2
– 20x – 7
40. 2x
2
– x - 36
Worksheet 30
Algebra Revision II
1.
2. 3x
3
3.
4.
5. 6x
5
6. 24y
9
7. 72x
4
8. 5x – 19
9. 10x – 22
10. -5x – 8
11. (x + 7)(x – 4)
12. (x + 8)(x + 2)
13. (x – 10)(x + 4)
14. (x – 15)(x – 5)
15. (x + 8)
2
16. (x – 2)
2
17. 2(x – 6)(x + 4)
18. 2(x + 7)(x + 4)
19. (x – 25)(x + 5)
20. (x + 60)(x + 40)
Worksheet 31
21. 15
22. 40
23. 24
24. 10.25
25. -8
26. -84
27. -13
28. -1350
29. 55
30. 30
31. 2x + 5
32. 3x – 3
33. -5x + 1
34. x + 2.5
35. x = -2
36. x = -0.5
37. (3x + 3)(x + 1)
38. x < -8
39. 3x
5
40. x = 2
Worksheet 32
Algebra Revision III
1. 5x – 5
2. 6x
2
+ 10x – 4
3. 3x – 5
4. x
2
– 6x + 9
5. –x + 16
6. 5y
2
+ 22y + 8
7. x = 5, 1
8. x = 0, 4
9. x = 4, -2
10. x = ±3/2
11. x = 8, -3
12. x = -10, 2
13. 6x
7
14. x + 3
15. 2y
16.
17. 16x
8
18.
19. (x – 40)
20. n = 4
Worksheet 33
21. A = 168.75, C = 45
22. S = 73
23. x + 8 × 150 = 1775
x = 575
24. (x – 5y)
25.
26.
40
When they collide, the DS-742ET will be there calculating it for you.
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