Edutest Year 8 Mathematics Practice

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

1. 1.A right-angled triangle has two shorter sides of 6cm and 8cm. What is the length of the longest side (hypotenuse)?

   • A10 cm
   • B12 cm
   • C14 cm
   • D100 cm
   Show answer and working

   Answer: A (10 cm)

   Use Pythagoras' theorem: c² = a² + b², where c is the hypotenuse. 6² + 8² = 36 + 64 = 100, and √100 = 10, so the hypotenuse is 10 cm. This is the 3-4-5 triangle doubled (6-8-10). The answer 14 adds the sides, and 100 forgets to take the square root.

2. 2.A car's price is reduced from $20,000 to $16,000. What is the percentage decrease?

   • A10%
   • B15%
   • C20%
   • D25%
   Show answer and working

   Answer: C (20%)

   Percentage decrease = decrease ÷ original × 100. The decrease is $20,000 − $16,000 = $4,000. Then 4,000 ÷ 20,000 = 0.2, which is 20%. The answer 25% comes from dividing by the new price ($16,000) instead of the original. Always compare the change to the starting value.

3. 3.If you roll a standard six-sided die twice, what is the most likely sum of the two rolls?

   • A2
   • B6
   • C7
   • D12
   Show answer and working

   Answer: C (7)

   There are 6 × 6 = 36 equally likely outcomes. A sum of 7 can be made in six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), more than any other total. A sum of 2 needs 1+1 and 12 needs 6+6, only one way each. A sum of 6 has five ways, so 7 is the most likely.

4. 4.If a = 2 and b = -3, what is the value of a² - b?

   • A1
   • B7
   • C-1
   • D4
   Show answer and working

   Answer: B (7)

   Substitute carefully, watching the negative sign. a² = 2² = 4. Then subtract b, which is −3: 4 − (−3). Subtracting a negative is the same as adding, so 4 + 3 = 7. The answer 1 treats it as 4 − 3, which ignores the negative sign on b.

5. 5.Simplify: 3(x + 2y) - 2(x - y)

   • Ax + 4y
   • Bx + 8y
   • C5x + 4y
   • Dx - 8y
   Show answer and working

   Answer: B (x + 8y)

   Expand each bracket, taking care with the minus sign. 3(x + 2y) = 3x + 6y. −2(x − y) = −2x + 2y, because −2 × −y = +2y. Now collect like terms: 3x − 2x = x and 6y + 2y = 8y. So the answer is x + 8y. Getting +2y rather than −2y is the key step.

6. 6.Find the median of these numbers: 5, 2, 8, 2, 9, 4, 7.

   • A2
   • B4
   • C5
   • D7
   Show answer and working

   Answer: C (5)

   The median is the middle value once the numbers are in order. Sorted, the list is 2, 2, 4, 5, 7, 8, 9. There are 7 numbers, so the middle one is the 4th, which is 5. A common mistake is to pick the middle of the unsorted list, which here would also be 2, so always sort first.

7. 7.What is the probability of flipping a coin and getting heads, AND rolling a die and getting a 6?

   • A1/6
   • B1/8
   • C1/12
   • D2/12
   Show answer and working

   Answer: C (1/12)

   The coin and the die are independent events, so multiply their probabilities. P(heads) = 1/2 and P(rolling a 6) = 1/6. P(both) = 1/2 × 1/6 = 1/12. There are 2 × 6 = 12 equally likely combinations, and only 'heads and 6' works. Adding the probabilities instead would be wrong.

8. 8.Find the area of a trapezium with parallel sides of 6cm and 10cm, and a height of 5cm.

   • A30 cm²
   • B40 cm²
   • C50 cm²
   • D80 cm²
   Show answer and working

   Answer: B (40 cm²)

   The area of a trapezium is the average of the parallel sides multiplied by the height: ½ × (a + b) × h. Here that is ½ × (6 + 10) × 5 = ½ × 16 × 5 = 8 × 5 = 40 cm². The answer 80 cm² forgets to halve, which gives the area of a rectangle twice as large.

9. 9.A map scale is 1:50000. A road on the map is 4cm long. How long is the actual road in km?

   • A0.2 km
   • B2 km
   • C20 km
   • D200 km
   Show answer and working

   Answer: B (2 km)

   A scale of 1:50 000 means 1 cm on the map is 50 000 cm in real life. So 4 cm represents 4 × 50 000 = 200 000 cm. Convert to kilometres: 200 000 cm ÷ 100 = 2000 m, and 2000 m ÷ 1000 = 2 km. Most errors come from the unit conversion, so convert one step at a time.

10. 10.Solve the simultaneous equations: x + y = 10 and x - y = 4.

    • Ax=7, y=3
    • Bx=6, y=4
    • Cx=5, y=5
    • Dx=8, y=2
    Show answer and working

    Answer: A (x=7, y=3)

    Add the two equations to eliminate y: (x + y) + (x − y) = 10 + 4, so 2x = 14 and x = 7. Substitute into x + y = 10: 7 + y = 10, so y = 3. Check in the second equation: 7 − 3 = 4. Option B also adds to 10, but its difference is only 2.