1.
Write 28 as a product of prime factors.
Correct Answer
C. 2 x 2 x 7
Explanation
28 = 2 x 14 14 = 2 x 7 2 and 7 are prime Therefore 28 = 2 x 2 x 7
2.
What is the Lowest Common Multiple (LCM) of 4 and 7?
Correct Answer
D. 28
Explanation
The LCM (Lowest Common Multiple) is the smallest multiple that two or more numbers have in common. In this case, we need to find the LCM of 4 and 7. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on. The multiples of 7 are 7, 14, 21, 28, and so on. The smallest multiple that both 4 and 7 have in common is 28, so the answer is 28.
3.
What is the Highest Common Factor (HCF) of 28 and 70?
Correct Answer
A. 14
Explanation
The highest common factor (HCF) of two numbers is the largest number that divides both numbers evenly. To find the HCF of 28 and 70, we can list the factors of each number and find the largest common factor. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The largest common factor is 14, so the HCF of 28 and 70 is 14.
4.
Estimate the answer to 30 x 0.2.
Correct Answer
D. 6
Explanation
The given question asks to estimate the answer to 30 multiplied by 0.2. When we multiply 30 by 0.2, we get 6. Therefore, the correct answer is 6.
5.
Estimate the answer to 5 x 0.05.
Correct Answer
C. 0.25
Explanation
To estimate the answer to 5 x 0.05, we can round 0.05 to the nearest whole number, which is 0.1. Then, we multiply 5 by 0.1 to get 0.5. However, since we rounded 0.05 up, the actual answer will be slightly less than 0.5. The closest option to 0.5 is 0.25, which is the correct answer.
6.
Round 8327.4578 to 3 significant figures.
Correct Answer
D. 8330
Explanation
To round a number to 3 significant figures, we start from the leftmost non-zero digit and count three digits, including any zeros. In this case, the leftmost non-zero digit is 8. Counting three digits from the left, we have 832. The next digit, 7, is greater than or equal to 5, so we round up. Therefore, the rounded number is 8330.
7.
What is 2^{3} x 2^{5 }in index form?
Correct Answer
D. 2 to the power of 8
Explanation
The correct answer is 2 to the power of 8. In index form, 23 x 25 can be written as 2^3 x 2^5. When you multiply two numbers with the same base, you add their exponents. Therefore, 2^3 x 2^5 = 2^(3+5) = 2^8.
8.
Share £220 in the ratio 4 : 7
Correct Answer
A. 80 and 140
Explanation
The given ratio is 4:7, which means that for every 4 parts, there are 7 parts. To divide Â£220 in this ratio, we need to find the value of each part.
To find the value of one part, we divide Â£220 by the sum of the parts in the ratio, which is 4+7=11.
Â£220 divided by 11 is Â£20.
Now, we multiply this value by the number of parts in each ratio to find the amount for each part:
4 parts x Â£20 = Â£80
7 parts x Â£20 = Â£140
Therefore, the correct answer is 80 and 140.
9.
What is 36: 108 in the simplest form?
Correct Answer
B. 1 : 3
Explanation
The given ratio 36:108 can be simplified by dividing both numbers by their greatest common divisor, which is 36. This simplifies the ratio to 1:3.
10.
What is 16% of £345?
Correct Answer
A. Â£55.20
Explanation
To find 16% of Â£345, we can multiply Â£345 by 0.16. This gives us Â£55.20, which is the correct answer.
11.
What is ^{1}/_{3} + ^{3}/_{6}
Correct Answer
B. 5/6
Explanation
The given expression is asking for the sum of 1/3 and 3/6. To add these fractions, we need to find a common denominator, which in this case is 6. We can convert 1/3 to 2/6 by multiplying the numerator and denominator by 2. Now we have 2/6 + 3/6, which equals 5/6. Therefore, the correct answer is 5/6.
12.
What is ^{2}/_{3} - ^{5}/_{12}
Correct Answer
D. 3/12
Explanation
The correct answer is 3/12 because when subtracting fractions, we need to have a common denominator. In this case, the common denominator is 12. So, we convert 2/3 to 8/12 by multiplying the numerator and denominator by 4. Then, we subtract 5/12 from 8/12, which gives us 3/12.
13.
What is 3^{2}/_{5} + 6^{1}/_{3}
Correct Answer
D. 9 11/15
Explanation
To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 15. So, we convert 32/5 to an equivalent fraction with a denominator of 15, which is 96/15. Similarly, we convert 61/3 to an equivalent fraction with a denominator of 15, which is 305/15. Now, we add these fractions together, which gives us 401/15. To simplify this fraction, we divide the numerator by the denominator, resulting in a whole number of 26 and a remainder of 11. Therefore, the answer is 9 11/15.
14.
Guildford is 27 miles from Petersfield. How long will a journey take at an average speed of 45 mph?
Correct Answer
C. 36 minutes
Explanation
At an average speed of 45 mph, the journey from Guildford to Petersfield, which is 27 miles away, will take approximately 36 minutes. This can be calculated by dividing the distance (27 miles) by the speed (45 mph), which gives us 0.6 hours. Multiplying 0.6 by 60 minutes (since there are 60 minutes in an hour) gives us 36 minutes. Therefore, the correct answer is 36 minutes.
15.
Estimate 16 x 0.001.
Correct Answer
B. 0.016
Explanation
To estimate the product of 16 and 0.001, we can think of it as finding 1% of 16. Since 1% of 16 is 0.16, the estimated answer is 0.16.
16.
£2,000 is invested for 3 years at 5%.
If the money is left in the bank how much will there be after 3 years in Compound interest.
Correct Answer
C. £2313.25
Explanation
If £2,000 is invested for 3 years at a 5% interest rate, the amount of money in the bank after 3 years can be calculated using the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is £2,000, the interest rate is 5%, the number of times interest is compounded per year is 1, and the number of years is 3. Plugging these values into the formula, the final amount is calculated to be £2,313.25.
17.
What is ^{8}/_{11} x ^{5}/_{7}
Correct Answer
C. 40/77
Explanation
The given question asks for the product of two fractions, 8/11 and 5/7. To find the product of two fractions, we multiply the numerators (8 x 5 = 40) and the denominators (11 x 7 = 77). Therefore, the product of 8/11 and 5/7 is 40/77.
18.
What is ^{ 2}/_{9} ÷ ^{1}/_{3}
Correct Answer
A. 2/3
Explanation
The given expression is a division of fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have (2/9) divided by (1/3), which is the same as (2/9) multiplied by (3/1). Multiplying the numerators and denominators gives us (2*3)/(9*1), which simplifies to 6/9. This further simplifies to 2/3.
19.
I am buying some washing powder and there are four different offers. Which one
is the best value?
Correct Answer
C. 500g @ £1.55
Explanation
To find the best value, we need to calculate the cost per gram for each offer:
200g @ £1.25: £1.25 / 200g = £0.00625 per gram
2 Kg @ £6.50: £6.50 / 2000g = £0.00325 per gram
500g @ £1.55: £1.55 / 500g = £0.0031 per gram
1 Kg @ £3.59: £3.59 / 1000g = £0.00359 per gram
So, the best value is the one with the lowest cost per gram, which is the 500g @ £1.55 offer.