Year 8 Math - Year Test Revision (Number And Algebra)

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| By Brad75
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Quizzes Created: 7 | Total Attempts: 13,083
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Year 8 Math - Year Test Revision (Number And Algebra) - Quiz

Questions and Answers
  • 1. 

    Use index laws to simplify:

    Correct Answer
    C.
  • 2. 

    Use index laws to simplify:

    Correct Answer
    B.
  • 3. 

    Use index laws to calculate:

    • A.

      1

    • B.

      2

    • C.

      9

    • D.

      90

    Correct Answer
    B. 2
    Explanation
    The given answer, 2, can be obtained by applying the index laws. Specifically, we can simplify the expression by multiplying the numbers together. 1 multiplied by 2 is 2, and 9 multiplied by 10 is 90. Then, multiplying 2 and 90 gives us the final result of 180.

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  • 4. 

    Calculate: 

    • A.

      11

    • B.

      1

    • C.

      -1

    • D.

      -7

    Correct Answer
    B. 1
  • 5. 

    Calculate:

    • A.

      13

    • B.

      -17

    • C.

      21

    • D.

      -13

    Correct Answer
    C. 21
  • 6. 

    Calculate:

    • A.

      -1

    • B.

      16

    • C.

      -8

    • D.

      8

    Correct Answer
    D. 8
    Explanation
    The given calculation involves a series of numbers. Starting from -1, the next number is obtained by multiplying the previous number by -2. Therefore, -1 x -2 = 2, and 2 x -2 = -4. Continuing this pattern, -4 x -2 = 8. Hence, the answer is 8.

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  • 7. 

    How would you represent following solution in an appropriate decimal format:

    Correct Answer
    D.
  • 8. 

    The shopkeeper reduces the price of a $70 pair of jeans by 20%.  How much do they now cost?

    • A.

      $68

    • B.

      $56

    • C.

      $50

    • D.

      $84

    Correct Answer
    B. $56
    Explanation
    The shopkeeper reduces the price of the jeans by 20%, which means that the price is now 80% of the original price. To find the new price, we can multiply the original price ($70) by 80% (0.8). This gives us a new price of $56.

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  • 9. 

    The same DVD is on sale in two different stores. Store A: DVD normally costs $34.95 but has a 1/3 off sale. Store B: DVD normally costs $29.95 and has a 25% off sale. Which store is cheaper?

    • A.

      Store A

    • B.

      Store B

    • C.

      Both are the same price

    Correct Answer
    B. Store B
    Explanation
    Store B is cheaper because the original price of the DVD is lower compared to Store A. Additionally, the discount percentage in Store B (25%) is higher than the discount percentage in Store A (1/3 off). Therefore, Store B offers a better deal and a lower price for the DVD.

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  • 10. 

    Sam was 160cm tall, but has grown by 5% in the last year.  How tall is Sam now?

    • A.

      160 cm

    • B.

      165 cm

    • C.

      168 cm

    • D.

      152.38 cm (2 decimal places)

    Correct Answer
    C. 168 cm
    Explanation
    Sam's height has increased by 5% in the last year. To find out his new height, we can calculate 5% of 160cm, which is 8cm. Adding this to his original height, we get 168cm. Therefore, Sam is now 168cm tall.

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  • 11. 

    Jo bought a bike for $200, fixed it up and then sold it for $250.  What percentage profit did Jo make?

    • A.

      10%

    • B.

      15%

    • C.

      20%

    • D.

      25%

    Correct Answer
    D. 25%
    Explanation
    Jo bought the bike for $200 and sold it for $250. To find the percentage profit, we need to calculate the difference between the selling price and the cost price, which is $250 - $200 = $50. Then, we divide this profit by the cost price and multiply by 100 to get the percentage. In this case, $50/$200 * 100 = 25%. Therefore, Jo made a 25% profit on the bike.

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  • 12. 

    Andrew bought a car for $15,000 and sold it a year later making a 10% loss.  How much did Andrew sell the car for?

    • A.

      $14,990

    • B.

      $14,850

    • C.

      $14,000

    • D.

      $13,500

    Correct Answer
    D. $13,500
    Explanation
    Andrew bought a car for $15,000 and made a 10% loss when he sold it a year later. To find out how much he sold the car for, we need to calculate 10% of the purchase price, which is $15,000 x 0.10 = $1,500. Then, we subtract this amount from the purchase price to find the selling price: $15,000 - $1,500 = $13,500. Therefore, Andrew sold the car for $13,500.

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  • 13. 

    Expand the following: 3(a - 2)

    • A.

      3a + 6

    • B.

      3a - 6

    • C.

      3a + 2

    • D.

      3a - 2

    Correct Answer
    B. 3a - 6
    Explanation
    The given expression is 3(a - 2). To expand this expression, we distribute the 3 to both terms inside the parentheses. This gives us 3 * a - 3 * 2, which simplifies to 3a - 6.

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  • 14. 

    Expand the following: 2(3b + 4)

    • A.

      6b + 8

    • B.

      5b + 6

    • C.

      6b + 4

    • D.

      23b + 24

    Correct Answer
    A. 6b + 8
    Explanation
    The given expression is 2(3b + 4). To expand it, we distribute the 2 to both terms inside the parentheses. This results in 6b + 8. Therefore, the correct answer is 6b + 8.

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  • 15. 

    Expand the following: c(4c + 5)

    Correct Answer
    D.
    Explanation
    The given expression can be expanded by multiplying the constant term outside the parentheses with each term inside the parentheses. Therefore, c(4c + 5) can be expanded as 4c^2 + 5c.

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  • 16. 

    Factorise the following: 6d - 12

    • A.

      6(d - 12)

    • B.

      3(2d - 4)

    • C.

      6d(1 - 12)

    • D.

      6(d - 2)

    Correct Answer
    D. 6(d - 2)
    Explanation
    The given expression, 6d - 12, can be factorized by taking out the common factor of 6 from both terms. This gives us 6(d - 2), which is the correct answer.

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  • 17. 

    Factorise the following:

    • A.

      X(3x + 9)

    • B.

      3(x + 3x)

    • C.

      3x(x + 3)

    • D.

      3(x + 3)

    Correct Answer
    C. 3x(x + 3)
    Explanation
    The given expression can be factorized by taking out the common factor, which is 3x. This results in 3x(x + 3).

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  • 18. 

    Factorise the following: 4y + 8z + 16

    • A.

      4y(8z + 16)

    • B.

      4(y + 2z + 4)

    • C.

      Y(4 + 8z + 16)

    • D.

      2(2y + 4z + 8)

    Correct Answer
    B. 4(y + 2z + 4)
    Explanation
    The given expression is 4y + 8z + 16. To factorize it, we can take out the common factor of 4 from each term, resulting in 4(y + 2z + 4).

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  • 19. 

    (2 + 4) + a x 2

    • A.

      12a

    • B.

      6a x 2

    • C.

      12 + a

    • D.

      6 + 2a

    Correct Answer
    D. 6 + 2a
    Explanation
    The given expression is (2 + 4) + a x 2. According to the order of operations (PEMDAS/BODMAS), we first perform the multiplication operation, which is a x 2. This gives us 2a. Then, we add the numbers inside the parentheses, which is 2 + 4, resulting in 6. Finally, we combine the two results to get 6 + 2a.

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  • 20. 

    • A.

      2a + 3

    • B.

      6a + 3

    • C.

      A

    • D.

      A + 3

    Correct Answer
    A. 2a + 3
  • 21. 

    • A.

      18ab - 10a

    • B.

      3a + 6b - 10a

    • C.

      18ab - 18a

    • D.

      -7a + 6b

    Correct Answer
    D. -7a + 6b
  • 22. 

    What is the missing number? x -2 -1 0 1 2 y -5 -3   1 3

    • A.

      -2

    • B.

      -1

    • C.

      0

    • D.

      1

    Correct Answer
    B. -1
    Explanation
    Looking at the pattern in the given numbers, it can be observed that the number on the left column is increasing by 1 each time, while the number on the right column is decreasing by 2 each time. Therefore, following the same pattern, the missing number should be -1.

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  • 23. 

    What is the missing number? x -3 -2 -1 0 1 y 10   4 1 -2

    • A.

      9

    • B.

      8

    • C.

      7

    • D.

      6

    Correct Answer
    C. 7
  • 24. 

    What is the equation for this line?

    • A.

      Y = 2x + 3

    • B.

      Y = 2x

    • C.

      Y = 3x + 2

    • D.

      Y = 3x

    Correct Answer
    A. Y = 2x + 3
    Explanation
    The equation for the given line is y = 2x + 3. This equation represents a straight line with a slope of 2 and a y-intercept of 3. The slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units. The y-intercept of 3 indicates that the line intersects the y-axis at the point (0, 3). Therefore, the equation y = 2x + 3 accurately represents the line.

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  • 25. 

    What is the equation for this line?

    • A.

      Y = 2x -2

    • B.

      Y = x - 2

    • C.

      Y = x

    • D.

      Y = x  - 2

    Correct Answer
    D. Y = x  - 2
    Explanation
    The equation of the line is y = x - 2. This can be determined by comparing the given equations with the equation of a line, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1 (since the coefficient of x is 1) and the y-intercept is -2. Therefore, the equation y = x - 2 represents the line.

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  • 26. 

    What is the equation for this line?

    • A.

      Y = x

    • B.

      Y = 2x

    • C.

      Y = 3x

    • D.

      Y = 4x

    Correct Answer
    C. Y = 3x
    Explanation
    The equation for the given line is y = 3x. This means that the value of y is always three times the value of x. For example, if x = 2, then y = 6. This equation represents a straight line with a slope of 3, meaning that for every increase of 1 in x, y increases by 3.

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  • 27. 

    What is the equation for this line?

    • A.

      Y = x + 4

    • B.

      Y = x - 4

    • C.

      Y = -x + 4

    • D.

      Y = -x - 4

    Correct Answer
    C. Y = -x + 4
    Explanation
    The equation of the line is y = -x + 4 because it has a slope of -1 and a y-intercept of 4. The negative slope indicates that the line is decreasing as x increases, and the positive y-intercept indicates that the line intersects the y-axis at the point (0, 4).

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