Edutest Year 7 Mathematics Practice

Try each question first, then open the worked solution to check your answer and see how to reach it.

1. 1.If 3x - 4 = 11, what is the value of x?

   • A3
   • B4
   • C5
   • D6
   Show answer and working

   Answer: C (5)

   Undo the operations in reverse order. First add 4 to both sides: 3x − 4 + 4 = 11 + 4, so 3x = 15. Then divide both sides by 3: x = 5. Check by substituting: 3 × 5 − 4 = 15 − 4 = 11, which is correct. The answer 4 forgets to add the 4 back before dividing.

2. 2.A train travels 180km in 2 hours. What is its average speed in km/h?

   • A60 km/h
   • B90 km/h
   • C120 km/h
   • D360 km/h
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   Answer: B (90 km/h)

   Average speed = distance ÷ time. The train covers 180 km in 2 hours, so 180 ÷ 2 = 90 km/h. In other words, it travels 90 km each hour. The answer 360 km/h multiplies instead of dividing, which gives a speed far too fast for 180 km in 2 hours.

3. 3.What is the value of 5² + 3³?

   • A19
   • B34
   • C52
   • D125
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   Answer: C (52)

   Work out each power separately before adding. 5² = 5 × 5 = 25 and 3³ = 3 × 3 × 3 = 27. Then add: 25 + 27 = 52. The answer 19 multiplies each base by its index (5 × 2 + 3 × 3), a common error. A power means repeated multiplication, not multiplying by the index.

4. 4.If a = 3 and b = 4, what is the value of 2a + b²?

   • A10
   • B14
   • C22
   • D25
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   Answer: C (22)

   Substitute a = 3 and b = 4 into the expression. 2a = 2 × 3 = 6. b² = 4 × 4 = 16. Then add: 6 + 16 = 22. The answer 14 treats b² as 2 × 4 = 8. Always calculate the power before adding, following the order of operations.

5. 5.The average of three numbers is 10. If two of the numbers are 8 and 12, what is the third number?

   • A8
   • B10
   • C12
   • D14
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   Answer: B (10)

   If the average of three numbers is 10, their total must be 3 × 10 = 30. The two known numbers add to 8 + 12 = 20, so the third number is 30 − 20 = 10. Check: (8 + 12 + 10) ÷ 3 = 30 ÷ 3 = 10. Turning an average back into a total is the key step.

6. 6.What is 15% of 60?

   • A6
   • B9
   • C12
   • D15
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   Answer: B (9)

   Build 15% from easier percentages. 10% of 60 is 60 ÷ 10 = 6. 5% is half of that, which is 3. So 15% = 6 + 3 = 9. Another way: 15% = 0.15, and 0.15 × 60 = 9. The answer 6 is only 10%, so make sure you add the extra 5%.

7. 7.What is the probability of drawing a Heart from a standard deck of cards?

   • A1/2
   • B1/4
   • C1/13
   • D1/52
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   Answer: B (1/4)

   A standard deck has 52 cards in four equal suits: hearts, diamonds, clubs and spades. That means 13 cards are hearts, so the probability is 13/52, which simplifies to 1/4. The answer 1/13 is the chance of drawing one particular rank, such as a king, and 1/52 is one specific card.

8. 8.What is the probability of flipping a coin 3 times and getting 3 heads?

   • A1/2
   • B1/4
   • C1/6
   • D1/8
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   Answer: D (1/8)

   Each flip is independent and has a 1/2 chance of heads. For three heads in a row, multiply the probabilities: 1/2 × 1/2 × 1/2 = 1/8. You can also list all outcomes: there are 2 × 2 × 2 = 8 possible results (HHH, HHT, HTH and so on), and only one is HHH.

9. 9.Calculate: 0.6 x 0.4

   • A0.24
   • B2.4
   • C0.024
   • D24
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   Answer: A (0.24)

   Multiply as whole numbers first: 6 × 4 = 24. Then count the decimal places in the question: 0.6 has one and 0.4 has one, which makes two in total. So the answer has two decimal places: 0.24. Estimating helps too: multiplying two numbers less than 1 gives an answer smaller than both.

10. 10.If a car travels at 60km/h, how far does it go in 45 minutes?

    • A30km
    • B40km
    • C45km
    • D50km
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    Answer: C (45km)

    45 minutes is three quarters of an hour (45 ÷ 60 = 0.75). At 60 km/h the car travels 60 km in one hour, so in three quarters of an hour it travels 0.75 × 60 = 45 km. At 60 km/h, the distance in km always equals the time in minutes, which is a handy check.