1.
Use index laws to simplify:
Correct Answer
C.
2.
Use index laws to simplify:
Correct Answer
B.
3.
Use index laws to calculate:
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.
4.
Calculate:
Correct Answer
B. 1
5.
Calculate:
Correct Answer
C. 21
6.
Calculate:
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.
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?
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.
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?
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.
10.
Sam was 160cm tall, but has grown by 5% in the last year. How tall is Sam now?
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.
11.
Jo bought a bike for $200, fixed it up and then sold it for $250. What percentage profit did Jo make?
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.
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?
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.
13.
Expand the following: 3(a - 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.
14.
Expand the following: 2(3b + 4)
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.
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.
16.
Factorise the following: 6d - 12
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.
17.
Factorise the following:
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).
18.
Factorise the following: 4y + 8z + 16
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).
19.
(2 + 4) + a x 2
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.
20.
Correct Answer
A. 2a + 3
21.
Correct Answer
D. -7a + 6b
22.
What is the missing number?
x
-2
-1
0
1
2
y
-5
-3
1
3
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.
23.
What is the missing number?
x
-3
-2
-1
0
1
y
10
4
1
-2
Correct Answer
C. 7
24.
What is the equation for this line?
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.
25.
What is the equation for this line?
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.
26.
What is the equation for this line?
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.
27.
What is the equation for this line?
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).