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Algebra Mastery Revision

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Algebra Mastery Revision

Simplify, substitute, expand, factorise and rearrange each expression or formula. Show your working where you can. Give units where needed.

Expressions and Substitution

1.Simplify: 7x + 4x − 3x.

2.Simplify: 5a − 8 + 3a + 11.

3.Expand: 4(2y − 3).

4.When x = 4 and y = −3, evaluate 3x + 2y.

5.When x = 4 and y = −3, evaluate x² − 2y.

6.When x = 4 and y = −3, evaluate 2(x − y) − 1.

7.Expand and simplify: 5(x + 2) − 3(x − 4).

8.Expand and simplify: (x + 4)(x + 1).

9.Factorise completely: 8x + 12.

10.Factorise completely: x² + 7x + 12.

11.Factorise completely: 3x² − 12x.

Changing the Subject

12.Rearrange y = 4x − 9 to make x the subject.

13.Rearrange Q = 3x + 2y to make x the subject.

14.Rearrange A = πr² to make r the subject. Assume r is non-negative.

15.Rearrange v = u + at to make t the subject.

16.Rearrange A = ½bh to make h the subject.

17.Rearrange E = mc² to make m the subject.

Algebra in Context

18.A streaming plan costs $18 per month, plus $0.15 for each extra download. Let d be the number of extra downloads and C the total cost in dollars. Write a formula for C in terms of d.

19.A streaming plan costs $18 per month, plus $0.15 for each extra download. Find the total cost when 120 extra downloads are made.

20.A streaming plan costs $18 per month, plus $0.15 for each extra download. If C is the total cost in dollars and d is the number of extra downloads, rearrange the formula for the total cost to make d the subject.

21.The formula F = 1.8C + 32 converts a temperature C in degrees Celsius to F in degrees Fahrenheit. Calculate F when C = 20.

22.Using the conversion formula F = 1.8C + 32, rearrange it to make C the subject.

23.The formula F = 1.8C + 32 converts a temperature C in degrees Celsius to F in degrees Fahrenheit. Find the Celsius temperature when F = 77°F.

24.The area of a trapezium is A = ½(a + b)h. Rearrange the formula to make b the subject.

25.A trapezium has area 72 cm², one parallel side of 10 cm, and a height of 8 cm. Use A = ½(a + b)h to calculate the length of its other parallel side.