National 5

Surds and Indices

100

Simplify √36

6

200

Simplify √128

8√2

300

a³ x a⁴

a⁷

400

(a⁵/a⁷)⁰

1

500

(a³)⁷ + a⁴

a²¹ + a⁴

Factorising

100

6x + 24

6(x + 4)

200

a² + 3a

a(a + 3)

300

5vw - 10vx

5v(w - 2x)

400

x² - 49

(x + 7)(x - 7)

500

x²  - 5x - 6

(x + 1)(x - 6)

Fractions

100

4/5 x 3/7

12/35

200

3/4 + 5/6

38/24

300

4/5 divided by 3/8

32/15

400

4(3/5) + 2(2/3)

109/15 OR 7(4/15)

500

2(5/6) divided by 2(1/2)

17/15 OR 1(2/15)

Vectors

100

If vector v = (2 4), what is 5v?

5v = (10 20)

200

If vector v = (6 7), what is |v|?

√84 OR 2√21

300

If vector v = (2 1 2) and vector p = (4 9 3), what is 

v + p?

v + p = (6 10 5)

400

If vector v = (8 9 2) and vector p = (4 3 5), what is 

3(v - p)?

3(v - p) = (12 18 -9)

500

If vector v = (1 3 7) and vector p = (2 7 2), what is 

|v - p|?

√42

Algebra

100

If a = 4 and b = 6, what is a² + b²?

52

200

3(t + 2)

3t + 6

300

If a=3, b=4 and c=2, what is a²(b +c)?

54

400

Expand (x - 5)²

x² - 10x + 25

500

Expand (2x + 4)(3x + 3)

6x² + 18x + 12