Question 1
1(a):
Simplify a^2 \times a^4
ANSWER: Multiple Choice (Type 2)
A: a^6
B: a^8
C: a^2
D: a^4
Answer: A
Workings:
a^2\times a^4 = a^{2+4} = a^6
Marks = 1
1(b):
Simplify \dfrac{b^6}{b^3}
ANSWER: Multiple Choice (Type 2)
A: b^3
B: b^2
C: b^{18}
D: b^9
Answer: A
Workings:
\dfrac{b^6}{b^3} = b^{6-3} = b^3
Marks = 1
1(c):
Work out 4\times 2^3
ANSWER: Simple Text Answer
Answer: 32
Workings:
4\times 2^3 = 4\times 8 = 32
Marks = 1
Question 2
2(a):
Simplify m^7 \times m^4
ANSWER: Multiple Choice (Type 2)
A: m^{11}
B: m^{28}
C: m^3
D: m^{14}
Answer: A
Workings:
m^7\times m^4 = m^{7+4} = m^{11}
Marks = 1
2(b):
Simplify \dfrac{m^7}{m^4}
ANSWER: Multiple Choice (Type 2)
A: m^3
B: m^{28}
C: m^{11}
D: m^{14}
Answer: A
Workings:
\dfrac{m^7}{m^4} = m^{7-4} = m^3
Marks = 1
2(c):
Work out 3^0
ANSWER: Simple Text Answer
Workings:
Anything to the power of 0 is equal to 1
3^0 = 1
Marks = 1
Question 3
3(a):
Simplify n^7\times n
ANSWER: Multiple Choice (Type 2)
A: n^8
B: n^6
C: n^7
D: n^9
Answer: A
Workings:
n^7\times n = n^{7+1} = n^8
Marks = 1
3(b):
Simplify \dfrac{p^6}{p^5}
ANSWER: Multiple Choice (Type 2)
A: p
B: p^{11}
C: p^{30}
D: p^{14}
Answer: A
Workings:
\dfrac{p^6}{p^5} = p^{6-5} = p
Marks = 1
3(c):
Simplify (2q^4)^5
ANSWER: Multiple Choice (Type 2)
A: 32q^{20}
B: 10q^9
C: 32q^9
D: 10q^{20}
Answer: A
Workings:
2^5 = 32
(q^4)^5 = q^{20}
(2q^4)^5 = 32q^{20}
Marks = 2
Question 4
4(a):
Simplify (3n^2)^3
ANSWER: Multiple Choice (Type 2)
A: 27n^6
B: 9n^5
C: 27n^5
D: 9n^6
Answer: A
Workings:
3^3 = 27
(n^2)^3 = n^6
(3n^2)^3 = 27n^6
Marks = 2
4(b):
Simplify (ag^7)^{14}
ANSWER: Multiple Choice (Type 2)
A: a^{14}g^{98}
B: a^{10}g^{94}
C: a^{20}g^{90}
D: a^{18}g^{96}
Answer: A
Workings:
(g^7)^{14} = g^{98}
(ag^7)^{14} = a^{14}g^{98}
Marks = 2
Question 5
5(a):
Simplify (9t^4)^2
ANSWER: Multiple Choice (Type 2)
A: 81t^8
B: 18t^6
C: 81t^6
D: 18t^8
Answer: A
Workings:
9^2 = 81
(t^4)^2 = t^8
(9t^4)^2 = 81t^8
Marks = 2
5(b):
Simplify \dfrac{24x^4y^{10}}{6x^2y^7}
ANSWER: Multiple Choice (Type 2)
A: 4x^2y^3
B: 4x^3y^2
C: 4x^4y^3
D: 4x^3y^4
Answer: A
Workings:
\dfrac{24}{6} = 4
\dfrac{x^4}{x^2} = x^2
\dfrac{y^{10}}{y^7} = y^3
\dfrac{24x^4y^{10}}{6x^2y^7} = 4x^2y^3
Marks = 2
Question 6
6(a):
Simplify 7a^2b^3\times 8a^4b^6
ANSWER: Multiple Choice (Type 2)
A: 56a^6b^9
B: 56a^8b^{18}
C: 56a^6b^{18}
D: 56a^8b^9
Answer: A
Workings:
7\times 8 = 56
a^2 \times a^4 = a^6
b^3\times b^6 = b^9
7a^2b^3\times 8a^4b^6 = 56a^6b^9
Marks = 2
6(b):
Simplify 8a^4b^6 \div 2a^2b^3
ANSWER: Multiple Choice (Type 2)
A: 4a^2b^3
B: 4a^6b^9
C: 4a^8b^{18}
D: 4a^2b^9
Answer: A
Workings:
\dfrac{8}{2} = 4
\dfrac{a^4}{a^2} = a^2
\dfrac{b^6}{b^3} = b^3
8a^4b^6 \div 2a^2b^3 = 4a^2b^3
Marks = 2
6(c):
Simplify (2ab)^2 \times 2a^4b^6
ANSWER: Multiple Choice (Type 2)
A: 8a^6b^8
B: 8a^8b^{12}
C: 8a^8b^6
D: 4a^8b^6
Answer: A
Workings:
(2ab)^2 = 4a^2b^2
4\times 2 = 8
a^2\times a^4 = a^6
b^2\times b^6 = b^8
(2ab)^2 \times 2a^4b^6 = 8a^6b^8
Marks = 2