Year 10 Exam Booklet: Algebra and Equations

[Pages:27]Year 10 Exam Booklet:

Algebra and Equations

Algebra and Equations

Easy

1. Express 1 - 1 as a single fraction.

3-2 3+2

Year 10 Mathematics Name: ..............................

2. Solve each quadratic equation using the method specified:

i.

2 + 3 + 1 = 0 by the quadratic formula,

ii.

2 - 2 - 1 = 0 by completing the square.

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Year 10 Mathematics

Algebra and Equations

Name: ..............................

3. Solve each of the following quadratic equation by the factorizing:

i.

2 + 4 = 0

ii.

2 + 11 - 26 = 0

iii.

22 - - 6 = 0

4. Simplify:

6

2

9 - 2 - 3 -

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Year 10 Mathematics

Algebra and Equations

5. Make r the subject in this equation: 3

= + 2

Name: ..............................

6. Solve 42 + 5 - 6 = 0

7. Solve each equation to find the value of x:

i.

3=4

5

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Algebra and Equations

ii.

3 - 5 = 5+

2

Year 10 Mathematics Name: ..............................

iii.

(3 - 5 = 5+

2

8. Solve these equations simultaneously for x and y: 5 - 2 = -16 3 + 4 = -7

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Year 10 Mathematics

Algebra and Equations

Name: ..............................

9. Solve 2(3 - ) 4 - and graph of the answer on a number line.

10. How many solutions does the quadratic equations 22 - 2 - 3 have?

(A). 0 (B). 1 (C). 2 (D). 3

11. Find the monic quadratic equation that has solutions = -4 and = 7. Give your answer in expanded form.

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Year 10 Mathematics

Algebra and Equations

Name: ..............................

12. If the equation = is rearranged to make r the subject of the formula, then

1-

the answer is:

(A). = 1 -

(B). = -

(C). = - 1

(D). = 1-

13. Solve the following simultaneous equations: = - 2 2 + = 7

14. Consider the quadratic 2 + + = 0. If the value of 2-4ac is less than zero, then the equation will have how many solutions?

(A). None (B). One (C). Two (D). Many

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Year 10 Mathematics

Algebra and Equations

Name: ..............................

15. A quadratic equation was solved to find that solutions were = 4 and = -4. What was the original equation?

(A). 2 + - 12 = 0 (B). 2 - - 12 = 0 (C). 2 - - 1 = 0 (D). 2 - 1 = 0

16. What is the correct solution to the equation 92 - 4 = 0?

(A). ? 2

3

(B). ? 3

2

(C). ? 4

9

(D). ? 9

4

17. Solve the following equations using the most appropriate methods 2 + 2 - 15 = 0

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