This page holds eleven original questions in rising difficulty, across number, algebra, geometry and data. Each answer is worked in full so you can compare your method, not just your result.
Attempt each question on paper first. Then open the answer and compare line by line. Every topic also has its own practice set inside its module, and the original mixed-practice builder can build a longer session.
How to use the set
- Work in a quiet block of 30 to 40 minutes.
- Write every step, even easy ones.
- Mark yourself honestly, then note the cause of each error: knowledge, interpretation or execution.
- Put each error in the mistake log.
Questions
Q1. Order from smallest to largest: −0.6, −2/3, −0.06, 1/2
Show answer
Convert: −2/3 ≈ −0.667 and 1/2 = 0.5. Negatives by distance from zero: −0.667 is furthest, then −0.6, then −0.06. Then the positive.
−2/3, −0.6, −0.06, 1/2
Q2. Work out 3/4 ÷ 2/5, giving an exact answer.
Show answer
Dividing by a fraction means multiplying by its reciprocal: 3/4 × 5/2 = 15/8.
15/8 (or 1 7/8)
Q3. Share RM 240 between Aina and Bala in the ratio 3 : 5.
Show answer
Total parts: 3 + 5 = 8. One part: 240 ÷ 8 = 30. Aina: 3 × 30 = 90. Bala: 5 × 30 = 150. Check: 90 + 150 = 240.
Aina RM 90, Bala RM 150
Q4. A bag costs RM 90 after a 20% increase. What was the price before the increase?
Show answer
After a 20% increase the price is 120% of the original, so original × 1.2 = 90. Original = 90 ÷ 1.2 = 75. Check: 75 × 1.2 = 90.
RM 75
Q5. A price of RM 50 rises by 40%, then the new price falls by 40%. Find the final price and the overall percentage change.
Show answer
Rise: 50 × 1.4 = 70. Fall: 70 × 0.6 = 42. Overall change: (42 − 50) ÷ 50 = −0.16.
RM 42, an overall decrease of 16%. The 40% fall is taken from a bigger base, so it removes more than the rise added.
Q6. Write 0.00072 in standard form.
Show answer
Move the decimal point until the number is between 1 and 10: 7.2. That took four places to the right, so the power is −4.
7.2 × 10⁻⁴
Q7. A length is 8.4 cm, correct to 1 decimal place. Write its lower and upper bounds.
Show answer
One decimal place means the rounding unit is 0.1, so the half-interval is 0.05.
Lower bound 8.4 − 0.05 = 8.35. Upper bound 8.4 + 0.05 = 8.45.
8.35 ≤ length < 8.45
Q8. Solve 3(x − 2) = 2x + 5.
Show answer
Expand: 3x − 6 = 2x + 5. Subtract 2x: x − 6 = 5. Add 6: x = 11.
Check: left side 3(11 − 2) = 27; right side 2(11) + 5 = 27.
x = 11
Q9. Solve the simultaneous equations 2x + y = 11 and x − y = 1.
Show answer
Add the equations to remove y: 3x = 12, so x = 4. Substitute into x − y = 1: 4 − y = 1, so y = 3.
Check in the first equation: 2(4) + 3 = 11.
x = 4, y = 3
Q10. A right-angled triangle has shorter sides 5 cm and 12 cm. Find the smaller acute angle, to 1 decimal place.
Show answer
The smaller angle is opposite the shorter side 5. The side 12 is adjacent. Use tan θ = opposite ÷ adjacent = 5/12.
θ = tan⁻¹(5/12) = 22.6° (to 1 d.p.).
Check: the hypotenuse is 13, and sin 22.6° = 5/13 ≈ 0.385, which matches.
22.6°
Q11. A car travels 150 km in 2 hours 30 minutes. Find its average speed in km/h.
Show answer
Convert the time to hours: 2 hours 30 minutes = 2.5 hours. Speed = distance ÷ time = 150 ÷ 2.5 = 60.
60 km/h
A common slip is writing 2.30 hours. Thirty minutes is half an hour, not 0.30 hours.
If you got these wrong
Route each error type to the lesson that repairs it.
| Question | If it went wrong | Go to |
|---|---|---|
| Q1 | Ordered negatives by their digits | Order signed numbers |
| Q2 | Multiplied by the original fraction, or cancelled wrongly | Fractions without decimal rounding |
| Q3 | Divided by 2 or by 3 instead of 8 | Share in a ratio |
| Q4 | Took 20% off 90 | Reverse a percentage increase |
| Q5 | Said the changes cancel | Why rise and fall do not cancel |
| Q6 | Wrong sign or count of places | Small measurements in standard form |
| Q7 | Used 0.1 instead of 0.05 | Recover an interval |
| Q8 | Sign error when expanding | Linear equations with brackets |
| Q9 | Subtracted when signs needed adding | Simultaneous relationships |
| Q10 | Used the wrong side pair | Right-triangle trigonometry |
| Q11 | Treated minutes as a decimal | Rates, time and compound quantities |
If you lost accuracy through early rounding, see the calculator accuracy help page. If you understood every step but could not start, see choosing a method.
When does practice need a teacher?
Some students read every answer here and still feel that the next question will go wrong in a new way. That is the point where listening to your reasoning helps more than another worksheet. In online one-to-one Mathematics tuition, a teacher can ask you to solve a problem aloud and notice where a sound idea turns into a wrong line.
For your route and scope, see the study route and revision page.