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Math 7

Math 7 · Worksheets

Year-end challenge

Ten questions of mixed difficulty, covering Circles and area, Data and probability, Divisibility and decimals, Equations, Fractions and percents. Print it, or work through it on screen — the answer key starts on its own page.

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Year-end challenge

Math 7 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A spinner has 4 equal sections: red, blue, green and yellow. In 100 spins it lands on red 29 times. Which statement is true?

    1. a) The experimental probability of red is 29%, and the theoretical probability is 25%.
    2. b) The spinner must be unfair, because red came up more than 25 times.
    3. c) The experimental probability of red is 25%, and the theoretical probability is 29%.
    4. d) The theoretical probability of red has now changed to 29%.

  2. On a pan balance, 3 identical bags of marbles balance 18 loose marbles. How many marbles are in each bag?

    1. a) 6
    2. b) 21
    3. c) 54
    4. d) 15

  3. Which list is in order from least to greatest?

    1. a) 0.3, 0.33, 0.334, 1/3
    2. b) 0.3, 1/3, 0.33, 0.334
    3. c) 0.3, 0.33, 1/3, 0.334
    4. d) 1/3, 0.3, 0.33, 0.334

  4. Solve 5x + 4 = 39.

    1. a) x = 7
    2. b) x = 35
    3. c) x = 8.6
    4. d) x = 3.8

  5. Which decimal is exactly equal to 2/3?

    1. a) 0.666…
    2. b) 0.6
    3. c) 1.5
    4. d) 0.67

  6. A school has 400 students. 35% of them take the bus and 25% get a ride in a car. The rest walk or bike. How many students walk or bike?

    1. a) 300
    2. b) 260
    3. c) 40
    4. d) 160

  7. Spinner A has three equal sections, 1, 2 and 3. Spinner B has two equal sections, 1 and 2. You spin both and add the numbers. What is the probability of a sum of 4?

    1. a) 1/3
    2. b) 1/6
    3. c) 1/4
    4. d) 2/5

  8. Which number is divisible by 8?

    1. a) 5128
    2. b) 2468
    3. c) 3148
    4. d) 7612

  9. A triangle has an area of 24 cm² and a base of 8 cm. What is its height?

    1. a) 12 cm
    2. b) 16 cm
    3. c) 6 cm
    4. d) 3 cm

  10. A $40 jacket is on sale for 15% off. What is the sale price?

    1. a) $6
    2. b) $46
    3. c) $34
    4. d) $25

Answer key · Year-end challenge

Math 7 · maddyhelps.com

  1. a) The experimental probability of red is 29%, and the theoretical probability is 25%. — Experimental probability comes from what happened, 29 out of 100; theoretical probability comes from the equally likely sections, 1 out of 4 = 25%. Real results wander: 29 reds in 100 spins is not unusual for a fair spinner, and spinning cannot change the theoretical probability.
  2. a) 6 — 3 bags balancing 18 marbles is the equation 3b = 18. Dividing both sides by 3 shares the 18 equally among the bags: b = 6. 15 subtracts the 3 instead of dividing, and 54 multiplies.
  3. c) 0.3, 0.33, 1/3, 0.334 — 1/3 = 0.333…, with the 3s going on forever. That is more than 0.33, but less than 0.334, which has a 4 in the thousandths place where 1/3 has a 3. Treating 1/3 as 0.3 puts it too early, and putting it last assumes a decimal that never ends must be bigger.
  4. a) x = 7 — Subtract 4 from both sides to get 5x = 35, then divide both sides by 5: x = 7. Check: 5 × 7 + 4 = 39 ✓. Adding 4 instead gives 43 ÷ 5 = 8.6, and 35 stops before dividing by 5.
  5. a) 0.666… — 2 ÷ 3 = 0.6666…, and the 6 repeats forever, so the exact value is 0.666…. 0.67 is that decimal rounded to hundredths — close, but not equal — and 1.5 is 3 ÷ 2.
  6. d) 160 — 35% + 25% = 60% ride, so 100% − 60% = 40% walk or bike, and 40% of 400 is 0.40 × 400 = 160. 40 is the percent, not the number of students the question asks for, and 260 or 300 takes away only one of the two groups that ride.
  7. a) 1/3 — A table has 3 × 2 = 6 equally likely outcomes, and two of them add to 4: 2 + 2 and 3 + 1. So the probability is 2/6 = 1/3. 1/4 counts the four possible sums, 2 to 5, as if they were equally likely, and 1/6 finds only one of the two ways to make 4.
  8. a) 5128 — For 8, test the last three digits, because 1000 = 8 × 125: 128 ÷ 8 = 16, so 5128 is divisible by 8. 3148 ends in 48, which 8 does divide, but looking at two digits is the rule for 4 — 148 ÷ 8 = 18.5, so 3148 is not.
  9. c) 6 cm — Area = b × h ÷ 2, so 8 × h ÷ 2 = 24. That means 8 × h = 48, and h = 6 cm. 3 cm divides 24 by 8 and forgets that the triangle is only half of 8 × h.
  10. c) $34 — 10% of $40 is $4, and 5% is half of that, $2, so 15% is $6. The sale price is $40 − $6 = $34. $6 is the discount, not the price, and $25 takes off 15 dollars instead of 15 percent.