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EN VIII Mathematics study materials
EN VIII Mathematics study resources

EN VIII Mathematics practice questions

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Question 1Numbers and operations

What is the value of 7 + 5 × 3 − 4?

  1. 32
  2. 18 Correct answer.
  3. 22
  4. 28

Explanation

Order of operations requires multiplication before addition and subtraction, so 5 × 3 = 15 first. Then 7 + 15 − 4 = 18, working left to right for the remaining operations.

Question 2Numbers and operations

Which of the following numbers is a prime number?

  1. 51
  2. 29 Correct answer.
  3. 57
  4. 91

Explanation

A prime has exactly two positive factors, 1 and itself. The number 29 has no factors other than 1 and 29, so it is prime.

Question 3Numbers and operations

What is the greatest common divisor of 36 and 60?

  1. 4
  2. 12 Correct answer.
  3. 6
  4. 18

Explanation

The greatest common divisor is the largest number dividing both values evenly. Factorising gives 36 = 2² × 3² and 60 = 2² × 3 × 5, so the shared product is 2² × 3 = 12.

Question 4Numbers and operations

Which fraction is equivalent to 0.375?

  1. 3/8 Correct answer.
  2. 3/4
  3. 1/3
  4. 5/8

Explanation

To convert a terminating decimal to a fraction, place the digits over the appropriate power of ten and simplify. Here 375/1000 reduces by dividing numerator and denominator by 125 to give 3/8.

Question 5Numbers and operations

What is the value of (−8) + (−5) − (−3)?

  1. −10 Correct answer.
  2. −16
  3. 0
  4. −6

Explanation

Adding two negatives gives −13, and subtracting a negative is equivalent to adding its positive. So −13 + 3 = −10.

Question 6Numbers and operations

What is 2³ × 2⁴ expressed as a single power of 2?

  1. 4⁷
  2. 2⁷ Correct answer.
  3. 2¹²
  4. 2¹

Explanation

When multiplying powers with the same base, add the exponents. Thus 2³ × 2⁴ = 2^(3+4) = 2⁷.

Question 7Numbers and operations

Which list is ordered from smallest to largest?

  1. 0.006, 0.06, 0.6 Correct answer.
  2. 0.06, 0.006, 0.6
  3. 0.6, 0.006, 0.06
  4. 0.6, 0.06, 0.006

Explanation

Compare decimals by their place values: 0.006 is six thousandths, 0.06 is six hundredths, and 0.6 is six tenths. Comparing place values gives the ascending order 0.006, 0.06, 0.6.

Question 8Numbers and operations

What is the value of √144?

  1. 72
  2. 14
  3. 12 Correct answer.
  4. 24

Explanation

A square root asks which number multiplied by itself gives the value. Since 12 × 12 = 144, the square root of 144 is 12.

Question 9Numbers and operations

What is 3/4 ÷ 2/5?

  1. 3/10
  2. 15/8 Correct answer.
  3. 6/20
  4. 8/15

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal. So 3/4 × 5/2 = 15/8, which cannot be simplified further.

Question 10Numbers and operations

A jacket costs $80. Its price is increased by 25%, then the new price is reduced by 20%. What is the final price?

  1. $84
  2. $80 Correct answer.
  3. $100
  4. $76

Explanation

An increase of 25% multiplies the price by 1.25, giving $100. A subsequent 20% reduction multiplies by 0.8, so $100 × 0.8 = $80, returning to the original price.

Question 11Numbers and operations

What is the lowest common multiple of 8 and 12?

  1. 48
  2. 96
  3. 4
  4. 24 Correct answer.

Explanation

The lowest common multiple is the smallest number divisible by both values. Multiples of 12 are 12, 24, 36..., and 24 is the first that is also a multiple of 8, so the answer is 24.

Question 12Numbers and operations

Express 0.00045 in scientific notation.

  1. 4.5 × 10⁴
  2. 4.5 × 10⁻³
  3. 45 × 10⁻⁵
  4. 4.5 × 10⁻⁴ Correct answer.

Explanation

Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten. Moving the decimal point four places right gives 4.5, so the exponent is −4.

Question 13Numbers and operations

Simplify (2x³)(3x⁴).

  1. 6x¹²
  2. 6x⁷ Correct answer.
  3. 5x⁷
  4. 6x⁵

Explanation

Multiply the coefficients and add the exponents of like bases. Here 2 × 3 = 6 and x³ × x⁴ = x^(3+4) = x⁷, giving 6x⁷.

Question 14Numbers and operations

A recipe uses sugar and flour in the ratio 2:5. If 350 g of flour is used, how much sugar is needed?

  1. 175 g
  2. 140 g Correct answer.
  3. 70 g
  4. 875 g

Explanation

Set up the proportion sugar/flour = 2/5. With 350 g of flour, sugar = (2/5) × 350 = 140 g.

Question 15Numbers and operations

What is the value of |−7| + |3 − 9|?

  1. 1
  2. 13 Correct answer.
  3. 10
  4. 4

Explanation

Absolute value gives the distance from zero, so |−7| = 7 and |3 − 9| = |−6| = 6. Their sum is 7 + 6 = 13.

Question 16Numbers and operations

Which number is irrational?

  1. √2 Correct answer.
  2. √16
  3. 0.75
  4. 22/7

Explanation

An irrational number cannot be written as a fraction of integers and has a non-terminating, non-repeating decimal. The square root of 2 is such a number, so it is irrational.

Question 17Numbers and operations

What is 5⁰ + 5¹?

  1. 0
  2. 10
  3. 6 Correct answer.
  4. 5

Explanation

Any nonzero number raised to the power 0 equals 1, and any number to the power 1 is itself. Thus 5⁰ + 5¹ = 1 + 5 = 6.

Question 18Numbers and operations

A number is increased by 40% to give 84. What was the original number?

  1. 60 Correct answer.
  2. 44
  3. 50.4
  4. 120

Explanation

An increase of 40% means the new value is 1.4 times the original. Dividing 84 by 1.4 gives 60, so the original number was 60.

Question 19Numbers and operations

What is 0.6 × 0.4?

  1. 0.24 Correct answer.
  2. 24
  3. 0.024
  4. 2.4

Explanation

Multiply the digits: 6 × 4 = 24. The factors have one and one decimal place respectively, so the product needs two decimal places, giving 0.24.

Question 20Numbers and operations

What is the value of 4! ÷ 3!?

  1. 4 Correct answer.
  2. 12
  3. 7
  4. 1

Explanation

The factorial n! is the product of all positive integers up to n. So 4! = 24 and 3! = 6, and 24 ÷ 6 = 4, which also follows from cancelling 3! in 4 × 3!/3!.

Question 21Numbers and operations

Which expression is equal to 2⁻³?

  1. 1/8 Correct answer.
  2. 8
  3. −8
  4. −6

Explanation

A negative exponent indicates the reciprocal of the corresponding positive power. Thus 2⁻³ = 1/2³ = 1/8.

Question 22Numbers and operations

A sum of money is shared among three people in the ratio 3:4:5. If the largest share is $60, what is the total amount shared?

  1. $180
  2. $120
  3. $135
  4. $144 Correct answer.

Explanation

The largest share corresponds to 5 parts, so each part is 60 ÷ 5 = $12. The total is 3 + 4 + 5 = 12 parts, giving 12 × 12 = $144.

Question 23Numbers and operations

What is the value of (2/3)⁻²?

  1. −9/4
  2. −4/9
  3. 4/9
  4. 9/4 Correct answer.

Explanation

A negative exponent takes the reciprocal of the base before applying the positive power. The reciprocal of 2/3 is 3/2, and (3/2)² = 9/4.

Question 24Numbers and operations

A shirt is discounted by 15%, and a further 10% is taken off the reduced price. If the final price is $61.20, what was the original price?

  1. $68
  2. $76.50
  3. $80 Correct answer.
  4. $72

Explanation

Successive discounts multiply: the final price is 0.85 × 0.90 = 0.765 of the original. Dividing 61.20 by 0.765 gives $80.

Question 25Numbers and operations

The number 2520 is divisible by every integer from 1 to 10. Which statement best explains why?

  1. It is the greatest common divisor of 1 through 10.
  2. It is the sum of the first ten integers.
  3. It is the product of the digits 1 through 10.
  4. It is the lowest common multiple of 1 through 10. Correct answer.

Explanation

The lowest common multiple of 1 through 10 is the smallest number divisible by each of them. Taking the highest power of each prime present (2³ × 3² × 5 × 7) gives 2520, so it is divisible by every integer from 1 to 10.

Question 26Numbers and operations

What is the value of 7 − (−4)?

  1. −3
  2. 3
  3. −11
  4. 11 Correct answer.

Explanation

Subtracting a negative number is the same as adding its positive value, so 7 − (−4) = 7 + 4 = 11.

Question 27Numbers and operations

Which of these is a prime number?

  1. 29 Correct answer.
  2. 33
  3. 27
  4. 21

Explanation

A prime has exactly two factors, 1 and itself; 29 has no factor other than 1 and 29. The other numbers are all divisible by 3.

Question 28Numbers and operations

What is the highest common factor of 36 and 48?

  1. 144
  2. 12 Correct answer.
  3. 6
  4. 4

Explanation

Writing 36 = 2² × 3² and 48 = 2⁴ × 3, the HCF takes the lowest power of each shared prime: 2² × 3 = 12.

Question 29Numbers and operations

What is 0.25 written as a fraction in simplest form?

  1. 1/25
  2. 1/4 Correct answer.
  3. 2/5
  4. 5/2

Explanation

0.25 means 25 hundredths, so 0.25 = 25/100. Dividing numerator and denominator by 25 gives 1/4.

Question 30Numbers and operations

What is the value of 3² + 2³?

  1. 13
  2. 10
  3. 25
  4. 17 Correct answer.

Explanation

Evaluate powers before adding: 3² = 9 and 2³ = 8, so the sum is 9 + 8 = 17.

Question 31Numbers and operations

Which number is a multiple of both 6 and 9?

  1. 27
  2. 12
  3. 54 Correct answer.
  4. 15

Explanation

A common multiple must be divisible by both 6 and 9; 54 = 6 × 9 and 54 = 9 × 6. The lowest common multiple of 6 and 9 is 18, and 54 is a multiple of 18.

Question 32Numbers and operations

What is the value of 2/3 + 1/6?

  1. 2/9
  2. 1/2
  3. 3/9
  4. 5/6 Correct answer.

Explanation

Rewrite 2/3 as 4/6 so both fractions share the denominator 6, then add: 4/6 + 1/6 = 5/6.

Question 33Numbers and operations

What is 4.8 ÷ 0.06?

  1. 0.8
  2. 800
  3. 8
  4. 80 Correct answer.

Explanation

Multiply both numbers by 100 to remove the decimal from the divisor: 4.8 ÷ 0.06 = 480 ÷ 6 = 80.

Question 34Numbers and operations

What is 2/5 written as a percentage?

  1. 40% Correct answer.
  2. 25%
  3. 45%
  4. 20%

Explanation

To convert a fraction to a percentage, multiply by 100: (2/5) × 100 = 40. So 2/5 equals 40%.

Question 35Numbers and operations

What is the value of (−3)² − (−2)³?

  1. 1
  2. −1
  3. 17 Correct answer.
  4. −17

Explanation

A negative number squared is positive, so (−3)² = 9; a negative number cubed stays negative, so (−2)³ = −8. Then 9 − (−8) = 9 + 8 = 17.

Question 36Numbers and operations

A quantity is multiplied by 1.08. Which single change does this represent?

  1. An increase of 8% Correct answer.
  2. A decrease of 8%
  3. An increase of 108%
  4. An increase of 0.8%

Explanation

A multiplier of 1 + r represents an increase of r expressed as a decimal. Since 1.08 = 1 + 0.08, the quantity rises by 0.08, which is 8%.

Question 37Numbers and operations

What is the value of 3/4 × 8/9, written in simplest form?

  1. 27/32
  2. 24/36
  3. 2/3 Correct answer.
  4. 11/13

Explanation

Multiply numerators and denominators: (3 × 8)/(4 × 9) = 24/36. Dividing both parts by 12 gives the simplest form 2/3.

Question 38Numbers and operations

What is the value of 5⁻² × 5⁴?

  1. 25 Correct answer.
  2. 125
  3. 5⁻⁸
  4. 5⁻⁶

Explanation

When multiplying powers with the same base, add the exponents: 5⁻² × 5⁴ = 5^(−2+4) = 5² = 25.

Question 39Numbers and operations

A car travels 240 km in 3 hours. At the same average speed, how far does it travel in 5 hours?

  1. 320 km
  2. 480 km
  3. 400 km Correct answer.
  4. 360 km

Explanation

The average speed is 240 ÷ 3 = 80 km/h. In 5 hours the car covers 80 × 5 = 400 km.

Question 40Numbers and operations

What is the value of √0.49?

  1. 0.07
  2. 0.7 Correct answer.
  3. 0.245
  4. 7

Explanation

Since 0.7 × 0.7 = 0.49, the square root of 0.49 is 0.7. The number of decimal places in the square is double that of its root.

Question 41Numbers and operations

Which of these numbers is divisible by 9?

  1. 4728
  2. 4726
  3. 4727
  4. 4725 Correct answer.

Explanation

A number is divisible by 9 exactly when its digit sum is divisible by 9. For 4725 the digits sum to 4 + 7 + 2 + 5 = 18, and 18 is divisible by 9.

Question 42Numbers and operations

A shirt costs $45 before tax and the sales tax rate is 8%. What is the total cost?

  1. $53.00
  2. $49.00
  3. $48.60 Correct answer.
  4. $45.36

Explanation

The tax is 8% of $45, which is 0.08 × 45 = $3.60. Adding this to the original price gives $45 + $3.60 = $48.60.

Question 43Numbers and operations

What is the value of (1/2)³ + (1/2)²?

  1. 1/2
  2. 3/8 Correct answer.
  3. 1/4
  4. 1/32

Explanation

Compute each power: (1/2)³ = 1/8 and (1/2)² = 1/4 = 2/8. Adding gives 1/8 + 2/8 = 3/8.

Question 44Numbers and operations

A number is written in prime factor form as 2³ × 3² × 5. How many positive divisors does the number have?

  1. 18
  2. 12
  3. 24 Correct answer.
  4. 30

Explanation

For a prime factorisation with exponents a, b, c, the number of divisors is (a+1)(b+1)(c+1). Here that gives (3+1)(2+1)(1+1) = 4 × 3 × 2 = 24.

Question 45Numbers and operations

A price is reduced by 20% and the new price is then increased by 25%. How does the final price compare with the original?

  1. It is 45% higher
  2. It is unchanged Correct answer.
  3. It is 5% higher
  4. It is 5% lower

Explanation

A 20% reduction uses the multiplier 0.8, and a 25% increase uses 1.25. Their product is 0.8 × 1.25 = 1, so the final price equals the original price.

Question 46Numbers and operations

What is the value of 0.00036 expressed in scientific notation?

  1. 3.6 × 10⁻⁵
  2. 3.6 × 10⁻⁴ Correct answer.
  3. 36 × 10⁻⁶
  4. 0.36 × 10⁻³

Explanation

Scientific notation writes a number as a × 10ⁿ with 1 ≤ a < 10. Moving the decimal point in 0.00036 four places right gives 3.6, so the exponent is −4.

Question 47Numbers and operations

The number N = 2⁵ × 5³ is written as an ordinary integer. How many zeros does N end in?

  1. 8
  2. 5
  3. 3 Correct answer.
  4. 2

Explanation

Each trailing zero comes from a factor of 10 = 2 × 5. The number of complete pairs of 2s and 5s is limited by the smaller exponent, min(5, 3) = 3, so N ends in 3 zeros.

Question 48Numbers and operations

Which statement about the product of a non-zero rational number and an irrational number is always true?

  1. It is zero
  2. It is irrational Correct answer.
  3. It is rational
  4. It is an integer

Explanation

If the product were rational, dividing by the non-zero rational factor would make the irrational factor rational, a contradiction. So the product must be irrational.

Question 49Numbers and operations

Which number is the greatest common divisor of 84 and 120?

  1. 840
  2. 6
  3. 24
  4. 12 Correct answer.

Explanation

Write each number in prime factor form: 84 = 2² × 3 × 7 and 120 = 2³ × 3 × 5. The GCD takes the lowest power of each shared prime, giving 2² × 3 = 12.

Question 50Numbers and operations

A number is decreased by 15%, and the result is 102. What was the original number?

  1. 135
  2. 117
  3. 120 Correct answer.
  4. 87

Explanation

A decrease of 15% leaves 85% of the original, so 0.85x = 102. Dividing both sides by 0.85 gives x = 120.