GCSEMathsAQAFoundationExam QuestionsAlgebraAlgebraic Roots & Indices

Algebraic Roots & Indices (AQA GCSE Maths: Foundation): Exam Questions

Exam code: 8300

50 mins30 questions
Easy
Medium
Hard
1
Sme Calculator1 mark

Find the value of  a to the power of 0

How did you do?

2
Sme Calculator1 mark

Simplify  x to the power of 1

How did you do?

3
Sme Calculator1 mark

Simplify  t to the power of 5 cross times t cubed

How did you do?

4
Sme Calculator1 mark

6 to the power of 10 cross times 6 to the power of x equals 6 squared

Find the value of x.

x equals........................

How did you do?

5
Sme Calculator1 mark

Find the value of x when 5 to the power of x cross times 5 cubed equals 5 to the power of 12

x equals............................

How did you do?

6a
Sme Calculator1 mark

Simplify.

p squared cross times p to the power of 4

How did you do?

6b
Sme Calculator1 mark

m to the power of 15 divided by m to the power of 5

How did you do?

6c
Sme Calculator1 mark

open parentheses k cubed close parentheses to the power of 5

How did you do?

7
Sme Calculator1 mark

9 to the power of 12 divided by 9 to the power of w equals 9 to the power of 4

Find the value of w.

w space equals................................

How did you do?

8
Sme Calculator1 mark

Simplify open parentheses w to the power of 5 close parentheses to the power of 4

How did you do?

9a
Sme Calculator1 mark

Simplify

t to the power of 21 divided by t to the power of 7

How did you do?

9b
Sme Calculator1 mark

open parentheses u to the power of 5 close parentheses to the power of 5

How did you do?

10
Sme Calculator1 mark

Simplify

open parentheses x to the power of 8 close parentheses cubed

How did you do?

11
Sme Calculator1 mark

Simplify.

open parentheses y to the power of 5 close parentheses cubed

How did you do?

12
Sme Calculator1 mark

Simplify open parentheses x to the power of 5 close parentheses squared.

How did you do?

13a
Sme Calculator1 mark

x cubed cross times x to the power of 6 equals x to the power of m

Find the value of m.

m = ................................................... 

How did you do?

13b
Sme Calculator1 mark

open parentheses x squared close parentheses to the power of n equals x to the power of 12

Find the value of n.

n = ................................................... 

How did you do?

1
Sme Calculator2 marks

Simplify  fraction numerator f to the power of 8 g cubed over denominator f squared g to the power of 6 end fraction

How did you do?

2
Sme Calculator2 marks

Simplify  3 x to the power of negative 7 end exponent cross times negative 6 x to the power of 5

How did you do?

3
Sme Calculator1 mark

open parentheses 3 to the power of 4 close parentheses to the power of n equals 3 to the power of 12

Find the value of n

 

n equals......................

How did you do?

4
Sme Calculator2 marks

i) 2 to the power of 8 cross times 2 to the power of m equals 2 to the power of 6 

Work out the value of m.

m = ................................................. [1]

ii) 5 to the power of n divided by 5 to the power of 4 equals 5 to the power of 6

Work out the value of n.

n = ................................................. [1]

How did you do?

5
Sme Calculator1 mark

Simplify.

5 cross times x to the power of 0

[1]

How did you do?

6
Sme Calculator2 marks

Simplify 2 x cubed cross times 3 x squared

How did you do?

7
Sme Calculator2 marks

Simplify.

5 m squared cross times 2 m cubed

How did you do?

8
Sme Calculator2 marks

(i) Find the value of k when x to the power of 10 divided by x to the power of k equals x cubed.

k space equals....................... [1]

(ii) Find the value of n when y to the power of 10 cross times y to the power of n equals 1.

n space equals......................... [1]

How did you do?

1a
Sme Calculator2 marks

Simplify  5 a to the power of 6 b cubed cross times 4 a to the power of negative 4 end exponent b to the power of 4

How did you do?

1b
Sme Calculator2 marks

Simplify  fraction numerator 18 x to the power of 8 y cubed over denominator 6 x to the power of 5 y to the power of 7 end fraction

How did you do?

2
Sme Calculator2 marks

10000 to the power of m cross times 1000 to the power of n can also be written in the form 10 to the power of y

Show that y equals 4 m plus 3 n

How did you do?

3
Sme Calculator2 marks

Simplify

open parentheses 2 f cubed g to the power of negative 2 end exponent close parentheses to the power of 5

How did you do?

4
Sme Calculator2 marks

Simplify.

4 p to the power of 5 q cubed space cross times p squared q to the power of negative 4 end exponent

How did you do?

5
Sme Calculator2 marks

Simplify 8 t to the power of 8 space divided by 4 t to the power of 4.

How did you do?

6
Sme Calculator2 marks

Simplify  x cubed y to the power of 4 cross times x to the power of 5 y cubed

How did you do?

7
Sme Calculator1 mark

Simplify

w to the power of 7 space divided by space w to the power of negative 2 end exponent

How did you do?

8
Sme Calculator1 mark

4 to the power of w space equals space 1 over 16

Find the value of w.

w space equals ...............................

How did you do?

9a1 mark

Simplify open parentheses a squared close parentheses to the power of 3 x end exponent

How did you do?

9b2 marks

Using your answer to part (a), simplify 2 to the power of x cross times 4 to the power of 3 x end exponent giving your answer as a single power of 2

How did you do?