Edutest Year 6 Mathematics Practice

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

1. 1.What is 20% of 150?

   • A20
   • B25
   • C30
   • D35
   Show answer and working

   Answer: C (30)

   20% means 20 out of 100, which is the same as one fifth. Find 10% first by dividing by 10: 150 ÷ 10 = 15. Then double it to get 20%: 15 × 2 = 30. Or divide by 5: 150 ÷ 5 = 30. Using 10% as a building block makes most percentage questions quick.

2. 2.If a bag contains 5 red balls and 10 blue balls, what is the probability of picking a red ball at random?

   • A1/2
   • B1/3
   • C1/4
   • D1/5
   Show answer and working

   Answer: B (1/3)

   Probability = favourable outcomes ÷ total outcomes. There are 5 red balls out of 5 + 10 = 15 balls in total, so the probability is 5/15. Simplify by dividing top and bottom by 5: 5/15 = 1/3. The answer 1/2 compares red with blue (5 to 10) instead of red with the total.

3. 3.A shop offers a 25% discount on a shirt that originally costs $40. What is the sale price?

   • A$10
   • B$20
   • C$30
   • D$35
   Show answer and working

   Answer: C ($30)

   25% is one quarter, so the discount is $40 ÷ 4 = $10. Subtract the discount from the original price: $40 − $10 = $30. The answer $10 is how much you save, not what you pay. You can also find 75% of $40 directly, because paying 100% − 25% = 75% gives $30.

4. 4.A map has a scale of 1cm : 5km. If two towns are 6cm apart on the map, what is the actual distance between them?

   • A11 km
   • B20 km
   • C30 km
   • D65 km
   Show answer and working

   Answer: C (30 km)

   The scale 1 cm : 5 km means every centimetre on the map stands for 5 kilometres in real life. The towns are 6 cm apart, so multiply: 6 × 5 = 30 km. The answer 11 km adds 6 + 5, which is a common mistake. Scale questions almost always need multiplication or division, not addition.

5. 5.A recipe for 12 cookies requires 200g of flour. How much flour is needed for 30 cookies?

   • A300g
   • B400g
   • C500g
   • D600g
   Show answer and working

   Answer: C (500g)

   Find the flour per cookie, or use a simpler step. 12 cookies need 200 g, so 6 cookies need 100 g. 30 cookies is 5 lots of 6, so 5 × 100 g = 500 g. Checking the ratio another way: 30 is 2.5 times 12, and 2.5 × 200 = 500 g.

6. 6.What is 3/4 + 1/8?

   • A4/12
   • B7/8
   • C5/8
   • D1/2
   Show answer and working

   Answer: B (7/8)

   To add fractions, the denominators must match. Change 3/4 into eighths by multiplying top and bottom by 2: 3/4 = 6/8. Then add: 6/8 + 1/8 = 7/8. The answer 4/12 adds tops and bottoms separately (3 + 1 and 4 + 8), which is a very common error.

7. 7.Calculate the area of a triangle with base 10cm and height 5cm.

   • A50 cm²
   • B25 cm²
   • C15 cm²
   • D30 cm²
   Show answer and working

   Answer: B (25 cm²)

   A triangle is half of a rectangle with the same base and height, so its area is ½ × base × height. Here that is ½ × 10 × 5 = ½ × 50 = 25 cm². The answer 50 cm² forgets to halve, which gives the area of the whole rectangle rather than the triangle.

8. 8.Solve for x: 2x + 3 = 11

   • A2
   • B3
   • C4
   • D5
   Show answer and working

   Answer: C (4)

   Work backwards to get x alone. Subtract 3 from both sides: 2x = 11 − 3 = 8. Then divide both sides by 2: x = 4. Check by substituting: 2 × 4 + 3 = 8 + 3 = 11, which is correct. Always undo the addition or subtraction before the multiplication.

9. 9.What is the complementary angle to 40°?

   • A40°
   • B50°
   • C140°
   • D90°
   Show answer and working

   Answer: B (50°)

   Complementary angles add up to 90°, a right angle. So the complement of 40° is 90° − 40° = 50°. The answer 140° is the supplementary angle, because supplementary angles add up to 180°. A memory trick: C comes before S in the alphabet, as 90 comes before 180.

10. 10.Round 3.56 to one decimal place.

    • A3.5
    • B3.6
    • C3.0
    • D4.0
    Show answer and working

    Answer: B (3.6)

    Rounding to one decimal place keeps the tenths digit, which is 5 in 3.56. Look at the next digit, the hundredths, which is 6. Because 6 is 5 or more, round the tenths up from 5 to 6, giving 3.6. The answer 3.5 cuts off the digit instead of rounding.