Question 1
LEVEL 3
Calculate the following:
(7+5)^2\div6^2-1
Select the correct answer from the options below:
A: 3
B: 575
C: \dfrac{121}{36}
D: \dfrac{144}{35}
CORRECT ANSWER: A: 3
WORKED SOLUTION:
Brackets take priority over indices, division, multiplication, addition or subtraction, hence we need to first calculate the value of the bracket:
(7+5)^2
Simple addition:
7+5=12
Indices or powers take priority over division, multiplication, addition or subtraction, hence:
12^2÷6^2-1=144\div36-1
Division takes priority over multiplication, addition or subtraction, hence:
144\div36-1=4-1=3
Answer = 3
Question 2
LEVEL 3
Evaluate (2\times3-4)\div5
Give your answer as a fraction in its simplest terms.
Select the correct answer from the options below:
A: \dfrac{6}{5}
B: \dfrac{-6}{5}
C: \dfrac{-2}{5}
D: \dfrac{2}{5}
CORRECT ANSWER: A: \dfrac{2}{5}
WORKED SOLUTION:
Brackets take priority over indices, division, multiplication, addition or subtraction, hence we need to first calculate the value of the bracket:
(2\times3-4)
Multiplication takes priority over addition or subtraction, hence:
2\times3-4=6-4=2
Simple division:
2\div5=\dfrac{2}{5}
Answer = \dfrac{2}{5}
Question 3
LEVEL 3
Evaluate (3\times5^2)\div5-20\times4+75
Give your answer as a fraction in its simplest terms.
Select the correct answer from the options below:
A: 55
B: -20
C: 35
D: 10
CORRECT ANSWER: A: 10
WORKED SOLUTION:
Brackets take priority over indices, division, multiplication, addition or subtraction, hence we need to first calculate the value of the bracket:
(3\times5^2)
Indices or powers take priority over division, multiplication, addition or subtraction, hence:
3\times5^2=3\times25
Simple multiplication:
3\times25=75
Division takes priority over multiplication, addition or subtraction, hence:
75÷5-20×4+75=15-20×4+75
Multiplication takes priority over addition or subtraction, hence:
15-20×4+75=15-80+75
Addition takes priority over subtraction, hence:
15-80+75=90-80=10
Answer = 10
Question 4
LEVEL 3
Evaluate 7+8+9-1+2-21+53
Select the correct answer from the options below:
A: 59
B: 55
C: 47
D: 57
CORRECT ANSWER: A: 57
WORKED SOLUTION:
Addition takes priority over subtraction, hence:
7+8+9-1+2-21+53=79-1-21
Simple subtraction:
79-1-21=57
Answer = 57
Question 5
LEVEL 3
Evaluate [(3^3 - 2^3 )+5]\div6\times4
Select the correct answer from the options below:
A: 1
B: 8
C: 16
D: 24
CORRECT ANSWER: C: 16
WORKED SOLUTION:
Brackets take priority over indices, division, multiplication, addition or subtraction, hence we need to first calculate the value of the bracket:
[(3^3 - 2^3 )+5]
Indices or powers take priority over division, multiplication, addition or subtraction, hence:
(3^3-2^3)=27-8=19
Simple addition:
[(3^3-2^3 )+5]=[19+5]=24
Division takes priority over multiplication, addition or subtraction, hence:
[(3^3-2^3 )+5]\div6\times4=24\div6\times4=4\times4
Simple multiplication:
4\times4=16
Answer = 16
Question 6
LEVEL 3
Evaluate 8\times9-49\div7-3\times1+3\times3
Select the correct answer from the options below:
A: 49
B: 64
C: 71
D: 19
CORRECT ANSWER: C: 71
WORKED SOLUTION:
Division takes priority over multiplication, addition or subtraction, hence:
8\times9-49\div7-3+1+3\times3= 8\times9-7-3+3\times3
Multiplication takes priority over addition or subtraction, hence:
8\times9-7-3+3\times3=72-7-3+9
Addition takes priority over subtraction, hence:
72-7-3+9=81-7-3=71
Answer = 71
Question 7
LEVEL 4
Calculate the value of x^3\times2-8^2\div2+3^2-10^2 when x = 5.
Select the correct answer from the options below:
A: 121
B: 127
C: -76
D: 96
CORRECT ANSWER: B: 127
WORKED SOLUTION:
Substitute x=5 into the expression, to get
5^3\times2-8^2\div2+3^2-10^2Indices or powers take priority over division, multiplication, addition or subtraction, hence:
5^3\times2-8^2\div2+3^2-10^2=125×2-64÷2+9-100
Division takes priority over multiplication, addition or subtraction, hence:
125×2-64 \div 2+9-100=125×2-32+9-100
Multiplication takes priority over addition or subtraction, hence:
125×2-32+9-100=250-32+9-100
Addition takes priority over subtraction, hence:
250-32+9-100=259-32-100=127
Answer = 127
Question 8
LEVEL 4
Calculate the value of [(x+11-9)^2+8.5\times2]\div 7 when x = 3
Select the correct answer from the options below:
A: 1
B: 2
C: 6
D: 7
CORRECT ANSWER: C: 6
WORKED SOLUTION:
Substitute x=3 into the expression, to get
[(3+11-9)^2+8.5\times2]\div 7Brackets take priority over indices, division, multiplication, addition or subtraction, hence we need to first calculate the value of the bracket:
[(3+11-9)^2+8.5\times2]
Brackets take priority over indices, division, multiplication, addition or subtraction, hence we need to first calculate the value of the bracket.
Inside the bracket (3+11-9)^2:
Addition takes priority over subtraction, hence:
3+11-9=14-9=5
Indices or powers take priority over division, multiplication, addition or subtraction, hence:
(3+11-9)^2+8.5\times2=5^2+8.5\times2=25+8.5\times2
Multiplication takes priority over addition or subtraction, hence:
25+8.5\times2=25+17=42
Division takes priority over multiplication, addition or subtraction, hence:
[(3+11-9)2+8.5\times2]\div7=42\div7=6
Answer = 6
Question 9
LEVEL 4
Write the expression (3y^2 + 4y^2) - 2y \times 5y in its simplest form.
Select the correct answer from the options below:
A: 7y^2 - 10y
B: 12y^4 - 10y^2
C: -3y^2
D: 3y^2
CORRECT ANSWER: C: -3y^2
WORKED SOLUTION:
Brackets take priority, hence:
(3y^2 + 4y^2) - 2y \times 5y = 7y^2 - 2y \times 5yThere are no indices or division, so multiplication takes the next priority:
7y^2 - 2y \times 5y = 7y^2 - 10y^2The last operation is subtraction:
7y^2 - 10y^2 = - 3y^2Answer = -3y^2