Interactive quiz

Mathematics entrance test

45 first-year secondary-school questions on fractions, powers, percentages and word problems.

45 randomly selected questions Pass mark: 60%

Instructions

45 questions in random order; answer choices are shuffled too. 1 point per correct answer, 0 for an incorrect or omitted answer. Maximum score: 45. Every solution is shown after submission.

A price is reduced by 25%, then by another 20% of the reduced price. What is the total discount from the original price?

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45% 50% 40% 36%

Simplify 5⁵ · 5⁻³ ÷ 5⁻⁶ · 5, from left to right.

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5⁹ 5⁻³ 5³ 5⁸

A quantity decreases by 20%, then increases by 20%. Compared with the start, the final quantity…

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stays the same increases depends on its initial value decreases

If x = 7/3, which expression is equivalent?

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8 − 1/3 1 − 4/3 3 − 2/3 7 + 1/3

Put 0.10, 4/3, recurring 0.1, 1/7 and 9/8 in increasing order.

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0,1̅ < 1/7 < 0,10 < 4/3 < 9/8 0,10 < 0,1̅ < 1/7 < 9/8 < 4/3 0,1̅ < 0,10 < 1/7 < 9/8 < 4/3 0,10 < 0,1̅ < 1/7 < 4/3 < 9/8

Simplify (−3/2)⁸ ÷ (2/3)³.

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(3/2)⁵ (−1)⁵ −(3/2)¹¹ (3/2)¹¹

What is 3/8 of 9/4?

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27/32 3/2 1/6 9/16

If a = −3, b = −7 and c = 4, what is a − b − c?

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6 0 −14 8

Simplify 2¹⁵ ÷ 2⁵.

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2¹⁰ 1¹⁰ 2³ 2²⁰

Three planes return to the same airport every 5, 10 and 6 days respectively. They leave together: after how many days will they return together?

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20 40 60 30

Which chain of inequalities is correct?

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1 > 2 > 3 1 < 2 < 3 1 < 2 > 3 1 ≤ 2 > 3

What is one third of 3¹⁸?

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3¹⁷ 3¹⁹ 3⁶ 1

What is 2 · (3/7) − (1/3)(3 − 6/7) + 1?

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12/7 5/7 15/7 8/7

A painter has painted 2/15 of a wall in 2 hours. How many more hours are needed to finish at the same rate?

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16 13 12 18

What is 11 − 2 ÷ 8 − 5?

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−31/8 3 23/4 31/3

What is (5 − 5)/10?

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1/10 5/2 impossible 0

10 workers finish a job in 15 days. How many days would 30 workers need at the same rate?

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10 3 5 6

Three cyclists complete a lap in 45, 60 and 36 minutes. They start together: after how long are they all back at the starting point?

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100 80 60 180

What is twice 2/3?

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1/3 4/3 4/9 4/6

What is 0.05 · (1/10)?

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5 0,5 0,005 0,050

The clock reads 15:10. What time will it show after the minute hand travels 1/5 of a full turn?

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15:33 15:55 15:15 15:22

What is 48.72 ÷ 24?

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2,3̅ 2,33 2,3 2,03

Which expression literally translates: “Divide the sum of 10 and the opposite of 2 by the difference between the product of 5 and 3 and the quotient of 12 and 4”?

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[10 + (−2)] : (5 · 3 − 12 : 4) 10 + (−2) : (5 · 3 − 12 : 4) (10 + 2) : (15 − 3) [10 + (−2)] : (12 : 4 − 5 · 3)

Which fraction equals 0.0042?

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21/50 42/100000 42/1000 21/5000

When is a fraction indeterminate?

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Numerator and denominator are equal The numerator is zero, the denominator is not Numerator and denominator are both zero The denominator is zero, the numerator is not

Evaluate (1/3) ÷ (1/4 + 1/5) · (10/3), working left to right for division and multiplication.

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2/3 1/9 200/81 10

What fraction represents recurring 2.3?

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23/90 7/3 2/3 23/9

What is −[(-3)²]³?

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−3⁵ 3⁶ 3⁵ −3⁶

Simplify (−3)⁷ ÷ 3³ · (−3)⁴, from left to right.

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−1 −3⁸ 0 1

14% of 22% of a number is 77. What is the number?

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800 2500 1250 1115

You have 90 minutes for a test and finish after 3/4 of that time. How long did you take?

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67 min 50 s 68 minutes 67 min 30 s 67 minutes

What is 2 − (−2)² − (−2)³?

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6 14 −2 −10

Shoes normally cost €120 and are sold at a 20% discount. Profit is 20% of the purchase cost: what is the profit in euros?

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19,20 € 16,00 € 24,00 € 17,60 €

Which decimal equals 20/8?

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2,50 2,4 5,2 20,8

One bartender makes 20 cocktails in 30 minutes. How many bartenders are needed to make 120 in one hour?

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3 6 4 2

Simplify 3³ · 3².

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3⁶ 9⁵ 6⁵ 3⁵

Cords of 28 m, 42 m and 35 m are cut into equal pieces of the greatest possible whole-metre length. What is each piece’s length, and how many physical cuts are needed in total?

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1 m; 105 cuts 5 m; 12 cuts 7 m; 15 cuts 7 m; 12 cuts

A dealer sells 100 cars in April. Sales rise by 10% in May and fall by 10% from May to June. How many cars are sold in June?

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101 111 99 100

A total price of €100 includes VAT at 4%. How much VAT is included, rounded to cents?

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104 € 3,85 € 4,00 € 3,60 €

Of 1,560 factory workers, 2/5 have at least two children; of these, 1/12 have more than two. How many have exactly two children?

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572 624 502 224

What is 3² + 5²?

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15² 8⁴ 8² 34

What is (4/5) ÷ (1/2)?

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8/5 2/10 8/10 2/5

What is twice 2¹⁵?

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4³⁰ 2³⁰ 2¹⁶ 4¹⁵

What is one hundredth of 100¹⁰⁰?

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100 99¹⁰⁰ 100⁹⁹ 1

6.9 km is 23% of a journey. How long is the whole journey?

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69 km 33 km 30 km 158,7 km

Have you completed the questions?

Submit your 45 answers to receive your score and review.