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Questions and Answers
1.
Select the correct inequality
A.
-3 ≤ x < 3
B.
-3 < x ≤ 3
C.
-3 ≤ x ≤ 3
D.
-3 < x < 3
Correct Answer A. -3 ≤ x < 3
Explanation The correct answer is -3 ≤ x < 3 because it represents a range of values for x that includes -3 and is less than 3. This means that x can be any value greater than or equal to -3 but less than 3.
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2.
Make a the subject of the formula: T= a - 6
A.
A = T - 6
B.
A = - 6 - T
C.
a = T + 6
D.
A = - 6 + T
Correct Answer C. a = T + 6
Explanation The given formula T = a - 6 can be rearranged to make a the subject by adding 6 to both sides of the equation. This gives us a = T + 6.
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3.
A steel ball has s volume of 1500cm^{3}.The density of the ball is 95g/cm^{3}Work out the mass of the ball in kg
Correct Answer 142.5,142.5 kg,142.5kg
Explanation The mass of an object can be calculated by multiplying its volume by its density. In this case, the volume of the steel ball is given as 1500 cm3 and the density is given as 95 g/cm3. To convert the volume to kg, we divide it by 1000 (since 1 kg = 1000 g). Therefore, the mass of the ball can be calculated as (1500 cm3 * 95 g/cm3) / 1000 = 142.5 kg.
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4.
To increase an amount by 18%, what single multiplier would you use?
A.
X 0.18
B.
X 1.82
C.
X 0.82
D.
X 1.18
Correct Answer D. X 1.18
Explanation To increase an amount by 18%, you would use a single multiplier of x 1.18. This is because multiplying the original amount by 1.18 will give you the increased amount, as 1.18 represents an increase of 18%.
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5.
To decrease an amount by 18%, what single multiplier would you use?
A.
X 0.18
B.
X 1.82
C.
X 0.82
D.
X 1.18
Correct Answer C. X 0.82
Explanation To decrease an amount by 18%, you would use a single multiplier of x 0.82. This is because multiplying the original amount by 0.82 would result in a decrease of 18% since 0.82 is equivalent to 82%.
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6.
Increase 380 by 18%
A.
68.4
B.
448.4
C.
311.6
Correct Answer B. 448.4
Explanation To increase a number by a certain percentage, we can multiply the number by 1 plus the percentage as a decimal. In this case, to increase 380 by 18%, we multiply 380 by 1 + 0.18 = 1.18. Therefore, the result is 380 * 1.18 = 448.4.
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7.
Decrease 380 by 18%
A.
68.4
B.
448.4
C.
311.6
Correct Answer C. 311.6
Explanation To decrease a number by a certain percentage, we multiply the number by (100% - the percentage). In this case, we multiply 380 by (100% - 18%), which is equivalent to multiplying by 82%. Therefore, 380 multiplied by 82% is equal to 311.6.
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8.
Round off 34162 to one significant figure
Correct Answer 30000
Explanation When rounding off a number to one significant figure, we look at the first non-zero digit from the left. In this case, the first non-zero digit is 3. Since we are rounding to one significant figure, we drop all the other digits after the first non-zero digit and replace them with zeros. Therefore, rounding off 34162 to one significant figure gives us 30000.
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9.
Without a calculator work out 0.6 ÷ 0.2
Correct Answer 3
Explanation To solve this division problem without a calculator, we need to divide 0.6 by 0.2. We can do this by multiplying both the numerator and denominator by 10 to get rid of the decimal point. So, 0.6 becomes 6 and 0.2 becomes 2. Now, we can divide 6 by 2, which gives us the answer of 3.
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10.
Estimate the answer to 109 ÷ 96
Correct Answer 1
11.
Without a calculator work out 0.4 x 0.6
Correct Answer 0.24
Explanation To calculate 0.4 x 0.6, we can multiply the two numbers together. When multiplying decimals, we ignore the decimal point and treat the numbers as whole numbers. So, 4 multiplied by 6 equals 24. Since there are two decimal places in the original numbers (0.4 and 0.6), we need to place the decimal point two places from the right in the answer. Therefore, the answer is 0.24.
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12.
Use a calculator to work out: √(3.6^{2} – 1.8^{2}) to 1dp
Correct Answer 3.1
Explanation To find the square root of a number, we need to calculate the square root of the difference between 3.62 and 1.82. Evaluating this difference gives us 1.8. Taking the square root of 1.8 to 1 decimal place gives us the answer of 3.1.
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13.
Use a calculator to work out to 1dp 15^{2} - 12^{2}√(9.6 - 3.78)
Correct Answer 33.6
Explanation To solve this problem, we first need to evaluate the expression inside the square root: 9.6 - 3.78 = 5.82. Taking the square root of 5.82 gives us approximately 2.41. Next, we subtract 122 times 2.41 from 152. This gives us 33.6. Therefore, the final answer is 33.6.
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14.
Expand & simplify (x - 3)(x - 4)
A.
X² + 7x - 12
B.
X² - 7x - 12
C.
X² - 7x + 12
D.
X² + 7x + 12
Correct Answer C. X² - 7x + 12
Explanation To expand and simplify (x - 3)(x - 4), we can use the distributive property. First, we multiply x by both terms in the second parentheses, giving us x^2 - 4x. Then, we multiply -3 by both terms in the second parentheses, giving us -3x + 12. Combining these terms, we have x^2 - 4x - 3x + 12, which simplifies to x^2 - 7x + 12.
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15.
Expand & simplify (x + 2)(x + 2)
A.
X² + 4x + 2
B.
X² + 4x + 4
C.
X² + 2x + 2
D.
X² + 2x + 4
Correct Answer B. X² + 4x + 4
Explanation To expand and simplify (x + 2)(x + 2), we can use the distributive property. First, we multiply x with both terms inside the second parentheses: x * x = x² and x * 2 = 2x. Then, we multiply 2 with both terms inside the second parentheses: 2 * x = 2x and 2 * 2 = 4. Finally, we combine like terms: x² + 2x + 2x + 4 = x² + 4x + 4. Therefore, the correct answer is x² + 4x + 4.
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16.
Solve: 3 x ≤ 6
A.
X ≤ 3
B.
X < 2
C.
X < 3
D.
X ≤ 2
Correct Answer D. X ≤ 2
Explanation The correct answer is x ≤ 2 because when we solve the inequality 3x ≤ 6, we divide both sides by 3 to isolate x. This gives us x ≤ 2, indicating that any value of x that is less than or equal to 2 will satisfy the inequality.
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17.
Work out the value of: 5x - 2y When x = 2 and y = -3
Correct Answer 16
Explanation To find the value of 5x - 2y, substitute the given values of x = 2 and y = -3 into the equation. So, 5(2) - 2(-3) equals 10 + 6 which equals 16. Therefore, the value of 5x - 2y when x = 2 and y = -3 is 16.
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18.
Write down the next term in this sequence: 2 5 11 20 32 ...
Correct Answer 47
19.
Write down the 5^{th} term in the sequence given by: T(n) = n^{2} - 7
Correct Answer 18
Explanation The 5th term in the sequence can be found by substituting n = 5 into the formula T(n) = n^2 - 7. Thus, T(5) = 5^2 - 7 = 25 - 7 = 18.
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20.
If y = x^{2} + 2x , find the value of y when x = 5
Correct Answer 35
Explanation When the value of x is substituted as 5 in the equation y = x^2 + 2x, we get y = 5^2 + 2(5) = 25 + 10 = 35. Therefore, the value of y when x = 5 is 35.
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21.
If y = x^{3} - 3 , find the value of y when x = 3
Correct Answer 24
Explanation When x = 3, substituting this value into the equation y = x^3 - 3, we get y = 3^3 - 3 = 27 - 3 = 24. Therefore, the value of y when x = 3 is 24.
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22.
Which calculation would you choose to find ‘d’ ?
A.
√(8² + 5²)
B.
√(8² - 5²)
Correct Answer B. √(8² - 5²)
Explanation To find 'd', we need to calculate the square root of the difference between 8 squared and 5 squared. This is because the Pythagorean theorem states that in a right triangle, the square of the hypotenuse (d) is equal to the sum of the squares of the other two sides. Therefore, we need to subtract the square of the shorter side (5) from the square of the longer side (8) and take the square root of the result.
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23.
10.2cm is rounded to one decimal place.Write down the minimum possible length it could have been.
Correct Answer 10.15cm, 10.15 cm, 10.15
Explanation The minimum possible length it could have been is 10.15cm because when rounding to one decimal place, any number less than 10.15cm would round down to 10.1cm.
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24.
If the relative frequency of a train being on time is 0.4, how often could you expect the train to be on time over 20days?
Correct Answer 8
Explanation If the relative frequency of a train being on time is 0.4, it means that out of every 10 trains, 4 trains are expected to be on time. Therefore, over a period of 20 days, we can expect 8 trains to be on time, as 4 trains being on time out of every 10 trains would translate to 8 trains being on time out of 20 trains.
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25.
Work out the volume of this prism? ( for ³ press ALT + 0179 )
Correct Answer 100, 100m³, 100 m³
Explanation The given answer options are all the same, indicating that the volume of the prism is 100 cubic meters.