Year 8 Maths Index and Factorising Simple Algebraic Expressions

Question 1

Write 342 as a product of its prime factors and in Index Form:

Answer 1

2 x 3^2 x 19 = 342

Question 2

Find the LCM and HCM between 45 and 16:

Answer 2

HCM = 1 and LCM = 720

Question 3

Round 24,671 to the 2nd Significant

Answer 3

25,000

Question 4

Simplify Expression 5(2x³+ 5x²-8)-3(4x²+5x+9)

Answer 4

10x³ -13x²-15x-67

Question 5

Rationilize 3/x+3 + 2/x-2 = -10/x+7

Answer 5

The first thing to do cross multiply and simplify and then cross multiply again. 15x^2+45x-60=0
x^2+3x+4
23-2x/5 = 3 x=-4 or x=1

Question 6

Simplify 6m^2/3m

Answer 6

Divide to get 2m

Question 7

Simplify 4(p+7)/(p+7)^2

Answer 7

Common Factor is (p+7) so it’s just 4/(p+7)

Question 8

Simplify x^2+5x+4/4x+16

Answer 8

Factor to get (x+1)(x+4)/4(x+4) answer is x+1/4

Question 9

What’s the hypotenuse when a = 4 and b = 7?

Answer 9

12+49 = 65 Square root of 8.2

Question 10

Simplify 1/5 (x-2)=3

Answer 10

x-2/5 = 3 x-2=15 17=x

Question 11

Simplify 1/4 x+6=-1

Answer 11

1/4x = -7 x 4 -28=x

Question 12

Simplify 3(x+5)/2 = 6

Answer 12

x = -1

Question 13

Simplify 2x-1/2 - x-5/3 = 5/4

Answer 13

Cross times an when you times the 6 by the right fraction times to top by 6 and divide 30 by 4 x=7.5

Question 14

Simplify 12/x+1 - 6/x-4 = -4

Answer 14

x = -3.5 or x = -5

Question 15

Simplify x/x+3 + 7/x-2 = 3

Answer 15

x=-3.9 or x = 4.94

Question 16

Simplify x/4 - 3x/4 = 1/2

Answer 16

x=-1

Question 17

Simplify x+7/6 = x/3

Answer 17

x=7

Question 18

Simplify x/6+2x/5 = 3

Answer 18

90/17 = x

Question 19

Simplify x+7/6 + 1/2 = x-2/4

Answer 19

x=26

Question 20

7(2/7+3x)=7(5)

Answer 20

32/21=x