Question 1

LEVEL 4

Simplify a^2 \times a^3

 

Select the correct answer from the list below:

A: a^6

B: a^5

C: a^1

D: 2a^5

 

CORRECT ANSWER: B: a^5

WORKED SOLUTION:

When multiplying algebra we,

multiply numbers like normal, so the invisible 1 in front of the a‘s is

1\times1=1

Then add the powers, so 2+3 = 5

This gives 1a^5 but we make the 1 invisible again in the final answer.

Question 2

LEVEL 4

Work out the value of \dfrac{a^3\times a^2}{a^{11}\div a^4}

 

Select the correct answer from the list below:

A: \dfrac{1}{a^5}

B: \dfrac{a^5}{a^7}

C: \dfrac{1}{a^2}

D: \dfrac{a}{a^2}

 

CORRECT ANSWER: C: \dfrac{1}{a^2}

WORKED SOLUTION:

When simplifying algebraic fractions such as this,

start by simplifying the numerator and denominator separately.

The numerator simplifies to a^5

The denominator simplifies to a^7

Then the numerator is divided by the denominator,

giving the answer \dfrac{1}{a^2}

Question 3

LEVEL 4

Work out 3^0

 

Select the correct answer from the list below:

A: x

B: 0

C: 3

D: 1

 

CORRECT ANSWER: D: 1

WORKED SOLUTION:

Remember the rule: Anything to the power 0 equals 1.

Question 4

LEVEL 4

Simplify (2p^3)^2

 

Select the correct answer from the list below:

A: 4p

B: 4p^6

C: 2p^6

D: 4p^5

 

CORRECT ANSWER: B: 4p^6

WORKED SOLUTION:

Bracket means multiply and power 2 means by itself

so you can multiple the bracket by itself

(2p^3)\times(2p^3)

We multiply numbers as normal and add the powers

to give 4p^6

Question 5

LEVEL 4

Simplify (3n^2)^3

 

Select the correct answer from the list below:

A: 9n^6

B: 27n^6

C: 9n^5

D: 27n^5

 

CORRECT ANSWER: B: 27n^6

WORKED SOLUTION:

The number in front of the n is

cubed like normal, giving 27

The powers are multiplied to get n^6

Giving the final answer 27n^6

Question 6

LEVEL 4

Simplify 10a^3b^3 \times 6a^2b

 

Select the correct answer from the list below:

A: 16a^5b^4

B: 60a^5b^4

C:  60a^5b^3

D:  60a^4b^5

 

CORRECT ANSWER: B: 60a^5b^4

WORKED SOLUTION:

Multiply the numbers like normal

so  10\times 6 = 60

Then add the powers of the same letters so,

a = 3 + 2 = 5
b = 3 + 1= 4

Bringing this together gives  60a^5b^4

Question 7

LEVEL 4

Simplify the expression:

\dfrac{x^4y^2z\times x^3yz^2}{xyz\times x^2y^2z^2}

 

Select the correct answer from the list below:

A: \dfrac{x^4y^2z}{xyz}

B: x^2

C: xyz^2

D:x^4

CORRECT ANSWER: D:x^4

WORKED SOLUTION:

Before we can simplify the fraction, we need to simplify the numerator and the denominator.

 

Numerator

When multiplying powers, we add the powers for the same letters

x^{(3+4)}\times y^{(2+1)}\times z^{(1+2)}=x^7y^3z^3

 

Denominator

Simplify the denominator in the same way you did the numerator.

x^{(1+2)}\times y^{(1+2)}\times z^{(1+2)}=x^3y^3z^3

 

Bring Together

And now we can substitute these into the original fraction.

\dfrac{x^4y^2z\times x^3yz^2}{xyz\times x^2y^2z^2}=\dfrac{ x^7y^3z^3 }{ x^3y^3z^3 }

We can now apply the division law, where you subtract powers.

Then do some cancelling to get the final answer, x^4

Question 8

LEVEL 4

Simplify the expression:

\dfrac{a^2b^3c^6\div (abc)}{a^2b^5c^3}

 

Select the correct answer from the list below:

A: \dfrac{c^3b}{a}

B: \dfrac{ac^2}{b^3}

C: abc^2

D: \dfrac{c^2}{ab^3}

 

CORRECT ANSWER: D: \dfrac{c^2}{ab^3}

WORKED SOLUTION:

Before we can simplify the fraction, we need to simplify the numerator.

 

Numerator

We can apply the division law and subtract the powers.

a^{(2-1)}\times b^{(3-1)}\times c^{(6-1)}=a^1b^2c^5=ab^2c^5

Substituting this into the original fraction gives:

\dfrac{a^2b^3c^6\div abc}{a^2b^5c^3} =\dfrac{ ab^2c^5 }{ a^2b^5c^3}

We can now apply the division law and do some cancelling by focusing on 1 letter at a time.

Each letter cancels down to give  \dfrac{c^2}{ab^3}