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

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

10%

15%

20%

25%

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.

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.

2) Use index laws to simplify:

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Explanation

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

$68

$56

$50

$84

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.

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.

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

160 cm

165 cm

168 cm

152.38 cm (2 decimal places)

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.

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.

5) What is the missing number?

x	-3	-2	-1	0	1
y	10		4	1	-2

9

8

7

6

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Explanation

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6) Expand the following: 2(3b + 4)

6b + 8

5b + 6

6b + 4

23b + 24

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.

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.

7) Use index laws to simplify:

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Explanation

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8) Calculate:

11

1

-1

-7

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Explanation

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9) Expand the following: c(4c + 5)

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.

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.

10) Match the ratios with the simplified ratio equivalent:

6:9

5:20

4:8

6:10

12:21

5:30

Submit

11) What is the missing number?

x	-2	-1	0	1	2
y	-5	-3		1	3

-2

-1

0

1

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.

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.

12) (2 + 4) + a x 2

12a

6a x 2

12 + a

6 + 2a

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.

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.

13) 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?

$14,990

$14,850

$14,000

$13,500

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.

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.

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

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Explanation

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15) 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?

Store A

Store B

Both are the same price

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.

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.

16) Expand the following: 3(a - 2)

3a + 6

3a - 6

3a + 2

3a - 2

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.

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.

17) What is the equation for this line?

Y = 2x -2

Y = x - 2

Y = x

Y = x - 2

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.

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.

18) What is the equation for this line?

Y = x

Y = 2x

Y = 3x

Y = 4x

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.

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.

19) What is the equation for this line?

Y = 2x + 3

Y = 2x

Y = 3x + 2

Y = 3x

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.

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.

20) Calculate:

-1

16

-8

8

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.

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.

21) Factorise the following: 4y + 8z + 16

4y(8z + 16)

4(y + 2z + 4)

Y(4 + 8z + 16)

2(2y + 4z + 8)

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).

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).

22)

2a + 3

6a + 3

A

A + 3

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Explanation

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23) Match the resulting number with the type of decimal.

Recurring

Terminating

Irrational

Submit

24) Calculate:

13

-17

21

-13

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Explanation

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25) Factorise the following:

X(3x + 9)

3(x + 3x)

3x(x + 3)

3(x + 3)

The given expression can be factorized by taking out the common factor, which is 3x. This results in 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).

26) Factorise the following: 6d - 12

6(d - 12)

3(2d - 4)

6d(1 - 12)

6(d - 2)

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.

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.

27) What is the equation for this line?

Y = x + 4

Y = x - 4

Y = -x + 4

Y = -x - 4

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).

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).

28) Match the resulting number with the type of decimal.

π

4÷9

2÷4

Submit

29)

18ab - 10a

3a + 6b - 10a

18ab - 18a

-7a + 6b

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Explanation

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30) Use index laws to calculate:

1

2

9

90

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.

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.