Algebraic Techniques (Year 8)

Language of Algebra

100

State how many terms there are:

7a + 2b + c

3

200

State the coefficient of b.

7 - 3a + b

1

300

State the coefficient of d.

4a - b + 3c - 4d

-4

400

Write an expression for half of q is subtracted from 5.

5 - 1/2q

500

The sum of b and c multiplied by the square of d

d²(b + c)

Substitution

100

Substitute a = 4 to evaluate a - 3.

1

200

Substitute a = 5 to evaluate 7a + 2.

37

300

Substitute a = -3 to evaluate -3a.

9

400

Substitute a = 4 and b = -3 into 8a - 3b.

41

500

Evaluate 4ab - 2b + 6c if a=-1, b=-3 and c=6.

54

Adding and Subtracting Terms

100

Simplify 7a + 12a by combining like terms.

19a

200

Simplify 11ab - 5ab + ba

7ab

300

Simplify 11b - 3b² + 5b² - 2b by combining like terms.

9b + 2b²

400

Simplify 10 + 7q - 3r + 2q - r by combining like terms.

10 + 9q - 4r

500

Simplify 7x²y + 5x - 10yx² - 5x

-3x²y

Multiplying and Dividing Terms

100

Simplify 8ab x 3c

24abc

200

Simplify -3ab x (-2b)

6ab²

300

Simplify 5a / 10a²

1 / 2a

400

Simplify 3a²b x 2a x 4b

24a³b²

500

-15z / -20z²

3 / 4z

Expanding

100

Expand 7(2a + 1)

14a + 7

200

Expand -8 (5 - h)

40 + 8h

300

Expand and Simplify:

7(9f + 10) + 2f

65f + 70

400

Expand and Simplify:

3(3 + 5d) + 4(10d + 7)

55d + 37

500

Expand and Simplify:

6 (10 - 6j) - 4(10j - 5)

80 - 76j