ACER Level P Mathematics Practice

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

1. 1.If 3 apples balance with 1 pear, and 2 pears balance with 1 melon, how many apples balance with 1 melon?

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

   Answer: C (6)

   Work through the balance one step at a time. 1 melon balances 2 pears. Each pear balances 3 apples, so 2 pears balance 2 × 3 = 6 apples. That means 1 melon balances 6 apples. Swapping one item for its equal amount at each step is the key to balance puzzles like this.

2. 2.Sam is taller than Max but shorter than Leo. Who is the tallest?

   • ASam
   • BMax
   • CLeo
   • DCannot be determined
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   Answer: C (Leo)

   Sam is taller than Max, so Max is below Sam. Sam is shorter than Leo, so Leo is above Sam. Putting them in order from tallest gives Leo, Sam, Max. So Leo is the tallest. Drawing three names in a line from tallest to shortest makes ordering questions easy to check.

3. 3.If tomorrow is Thursday, what day was yesterday?

   • AMonday
   • BTuesday
   • CWednesday
   • DFriday
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   Answer: B (Tuesday)

   Start from a day you know. If tomorrow is Thursday, today must be Wednesday. Yesterday is the day before today, so yesterday was Tuesday. Writing the days in order (Tuesday, Wednesday, Thursday) and marking yesterday, today and tomorrow avoids counting mistakes.

4. 4.At a farm, there are 4 cows and 3 chickens. How many legs are there in total?

   • A14
   • B16
   • C20
   • D22
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   Answer: D (22)

   Count the legs for each kind of animal, then add. Cows have 4 legs, so 4 cows have 4 × 4 = 16 legs. Chickens have 2 legs, so 3 chickens have 3 × 2 = 6 legs. Altogether there are 16 + 6 = 22 legs. The answer 14 gives every animal 2 legs.

5. 5.Box A has 10 marbles. Box B has 5 more marbles than Box A. Box C has double the amount of Box B. How many marbles are in Box C?

   • A15
   • B20
   • C25
   • D30
   Show answer and working

   Answer: D (30)

   Follow the boxes in order. Box A has 10 marbles. Box B has 5 more than A, so it has 10 + 5 = 15. Box C has double Box B, so it has 15 × 2 = 30. The answer 20 doubles Box A instead of Box B, so read carefully which box each step refers to.

6. 6.Emma is 8 years old. Her brother is half her age. How old will her brother be when Emma turns 12?

   • A6
   • B8
   • C10
   • D12
   Show answer and working

   Answer: B (8)

   Emma's brother is half of 8, so he is 4 now. The difference between their ages is 8 − 4 = 4 years, and it always stays the same. Emma turns 12 in 4 years, and her brother will also be 4 years older: 4 + 4 = 8. He will not still be half her age.

7. 7.If 1 blip equals 3 blops, and 1 blop equals 2 glips, how many glips are in 1 blip?

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

   Answer: C (6)

   Change one unit at a time. 1 blip equals 3 blops. Each blop equals 2 glips, so 3 blops equal 3 × 2 = 6 glips. That means 1 blip equals 6 glips. The made-up words do not matter; the question tests whether you multiply through each exchange step.

8. 8.I am thinking of a number. I double it, add 4, and get 14. What is the number?

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

   Answer: B (5)

   Work backwards and undo each step. The last step was adding 4, so take 4 away: 14 − 4 = 10. The first step was doubling, so halve it: 10 ÷ 2 = 5. Check by going forwards: 5 doubled is 10, and 10 + 4 = 14.

9. 9.A clock is 15 minutes fast. It currently shows 2:30. What is the real time?

   • A2:15
   • B2:45
   • C3:00
   • D3:15
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   Answer: A (2:15)

   A clock that is 15 minutes fast shows a time that is ahead of the real time. To find the real time, go back 15 minutes from what the clock shows: 2:30 − 15 minutes = 2:15. The answer 2:45 adds the 15 minutes, which would be right only if the clock were slow.

10. 10.How many hours are there in 2 and a half days?

    • A48 hours
    • B54 hours
    • C60 hours
    • D72 hours
    Show answer and working

    Answer: C (60 hours)

    There are 24 hours in one day. Two days is 24 + 24 = 48 hours, and half a day is 12 hours. Altogether, 48 + 12 = 60 hours. You can also multiply: 2.5 × 24 = 60. The answer 48 forgets the extra half day.