ACER Level 1 Mathematics Practice

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

1. 1.What number is halfway between 1/4 and 1/2?

   • A1/3
   • B3/8
   • C3/4
   • D5/8
   Show answer and working

   Answer: B (3/8)

   Halfway between two numbers is their average. Write both with the same denominator: 1/4 = 2/8 and 1/2 = 4/8. Halfway between 2/8 and 4/8 is 3/8. You can also add them and halve: (1/4 + 1/2) ÷ 2 = (3/4) ÷ 2 = 3/8. The answer 1/3 is close but not exactly halfway.

2. 2.Which is the largest?

   • A3/5
   • B5/8
   • C0.65
   • D62%
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   Answer: C (0.65)

   Convert every option to a decimal so you can compare them. 3/5 = 0.6, 5/8 = 0.625, 0.65 stays as it is, and 62% = 0.62. The largest is 0.65. Mixed formats are designed to confuse, so changing everything into one form is the safest method.

3. 3.The ratio of boys to girls is 3:4. If there are 28 girls, how many boys?

   • A18
   • B21
   • C24
   • D32
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   Answer: B (21)

   A ratio of 3:4 means 3 boys for every 4 girls. There are 28 girls, so each 'part' of the ratio is 28 ÷ 4 = 7 students. Boys have 3 parts: 3 × 7 = 21 boys. Check: 21:28 simplifies to 3:4 when you divide both by 7.

4. 4.Find x if 4:x :: 12:21

   • A6
   • B7
   • C8
   • D9
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   Answer: B (7)

   The proportion 4 : x = 12 : 21 means both ratios are equal. 12 is 3 times 4, so 21 must be 3 times x. That gives x = 21 ÷ 3 = 7. Check by simplifying 12:21 by dividing both by 3, which gives 4:7. Looking for the scale factor is quicker than cross-multiplying.

5. 5.A train leaves at 10:45 and arrives at 13:15. Journey time?

   • A2h 15m
   • B2h 30m
   • C2h 45m
   • D3h
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   Answer: B (2h 30m)

   Count on in steps. From 10:45 to 11:00 is 15 minutes. From 11:00 to 13:00 is 2 hours. From 13:00 to 13:15 is 15 more minutes. Total: 2 hours and 30 minutes. 24-hour time is used here, so 13:15 is 1:15 pm.

6. 6.Simplify: 2(3x - 1) - 3(x + 2)

   • A3x - 4
   • B3x - 8
   • C9x - 8
   • D3x + 4
   Show answer and working

   Answer: B (3x - 8)

   Expand each bracket, taking care with the second sign. 2(3x − 1) = 6x − 2. −3(x + 2) = −3x − 6, because the minus applies to both terms. Combine like terms: 6x − 3x = 3x and −2 − 6 = −8. So the answer is 3x − 8. Option A forgets to multiply the 2 by −3.

7. 7.How many edges in a triangular prism?

   • A6
   • B8
   • C9
   • D12
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   Answer: C (9)

   A triangular prism has two triangle ends joined by three rectangles. Each triangle has 3 edges, which makes 6 edges for the two ends. Three more edges join the matching corners of the triangles. Total: 6 + 3 = 9 edges. It also has 6 vertices and 5 faces.

8. 8.A piece of rope 2m long is cut into 3 pieces in ratio 2:3:5. Length of longest piece?

   • A60cm
   • B80cm
   • C100cm
   • D120cm
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   Answer: C (100cm)

   First change 2 m into 200 cm so the answer matches the options. The ratio 2:3:5 has 2 + 3 + 5 = 10 parts, so each part is 200 ÷ 10 = 20 cm. The longest piece has 5 parts: 5 × 20 = 100 cm. Check: 40 + 60 + 100 = 200 cm.

9. 9.A vendor buys for $15, sells for $20. Profit percentage?

   • A25%
   • B30%
   • C33.3%
   • D40%
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   Answer: C (33.3%)

   Profit percentage is based on the cost price. The profit is $20 − $15 = $5. As a percentage of the cost: 5 ÷ 15 = 1/3, which is about 33.3%. The answer 25% divides the profit by the selling price ($20) instead of the cost, which is the most common mistake.

10. 10.Number of diagonals in a pentagon?

    • A4
    • B5
    • C6
    • D7
    Show answer and working

    Answer: B (5)

    A diagonal joins two corners that are not next to each other. From each of the 5 corners you can draw diagonals to 2 other corners, giving 5 × 2 = 10. But each diagonal is counted from both ends, so divide by 2: 10 ÷ 2 = 5 diagonals. The formula n(n − 3)/2 gives the same result.