Key Stage 3 Mental Arithmetic Test

1) 7a + 2b + 3a + 5b =

17ab

10a + 7b

9ab + 8ab

9a + 8a

The given equation is 7a + 2b + 3a + 5b. We can combine like terms by adding the coefficients of the same variables. So, combining the coefficients of 'a', we get 7a + 3a = 10a. Similarly, combining the coefficients of 'b', we get 2b + 5b = 7b. Therefore, the simplified form of the equation is 10a + 7b, which matches the given answer.

Explanation

The given equation is 7a + 2b + 3a + 5b. We can combine like terms by adding the coefficients of the same variables. So, combining the coefficients of 'a', we get 7a + 3a = 10a. Similarly, combining the coefficients of 'b', we get 2b + 5b = 7b. Therefore, the simplified form of the equation is 10a + 7b, which matches the given answer.

2) 2f + f = 30
What Does f Equal To ?

8

10

0.1

11

In the given equation, 2f + f = 30, we need to find the value of f. Combining like terms, we get 3f = 30. Dividing both sides by 3, we find that f = 10.

Explanation

In the given equation, 2f + f = 30, we need to find the value of f. Combining like terms, we get 3f = 30. Dividing both sides by 3, we find that f = 10.

3) - 170 + 19 =

The given equation is 170 + 19. When we add 170 and 19 together, we get a sum of 189. However, the given answer is -151, which is incorrect. The correct answer should be 189.

Explanation

The given equation is 170 + 19. When we add 170 and 19 together, we get a sum of 189. However, the given answer is -151, which is incorrect. The correct answer should be 189.

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4) 13kd
If k = 3 and d = 2
Then What does 13kd equal?

The expression 13kd can be simplified by substituting the given values of k and d. Since k = 3 and d = 2, we can rewrite 13kd as 13(3)(2). Multiplying these values together gives us 78, which is the final result.

Explanation

The expression 13kd can be simplified by substituting the given values of k and d. Since k = 3 and d = 2, we can rewrite 13kd as 13(3)(2). Multiplying these values together gives us 78, which is the final result.

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5) If 48 x 72 = 3456
What Is 24 x 72 ?

1223

864

1728

3456

The given equation states that 48 multiplied by 72 equals 3456. To find the product of 24 multiplied by 72, we can observe that 24 is half of 48. Therefore, the product will also be half of 3456. Half of 3456 is 1728.

Explanation

The given equation states that 48 multiplied by 72 equals 3456. To find the product of 24 multiplied by 72, we can observe that 24 is half of 48. Therefore, the product will also be half of 3456. Half of 3456 is 1728.

6) Write 1/8 as a Decimal

To convert a fraction to a decimal, we divide the numerator (1) by the denominator (8). In this case, 1 divided by 8 equals 0.125. Therefore, the decimal representation of 1/8 is 0.125.

Explanation

To convert a fraction to a decimal, we divide the numerator (1) by the denominator (8). In this case, 1 divided by 8 equals 0.125. Therefore, the decimal representation of 1/8 is 0.125.

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7) Y x y x y x y =

4y

Y to the power of 4

Yyyy

1

The given expression is a sequence of y and x repeated multiple times. The pattern suggests that every y is multiplied by x, resulting in the next y. This process is repeated four times, so the final expression is y to the power of 4.

Explanation

The given expression is a sequence of y and x repeated multiple times. The pattern suggests that every y is multiplied by x, resulting in the next y. This process is repeated four times, so the final expression is y to the power of 4.

8) Estimate What 59.8 divided by 2.99

20

30

25

35

To estimate 59.8 divided by 2.99, we can round both numbers to the nearest whole number. 59.8 rounds to 60, and 2.99 rounds to 3. Dividing 60 by 3 gives us 20. Therefore, the estimated answer is 20.

Explanation

To estimate 59.8 divided by 2.99, we can round both numbers to the nearest whole number. 59.8 rounds to 60, and 2.99 rounds to 3. Dividing 60 by 3 gives us 20. Therefore, the estimated answer is 20.

9) 36 : 9 Simlify This Down To It's Simpliest Form

4

4 : 1

4 : 3

12 : 3

The given expression "36 : 9" can be simplified by dividing both numbers by their greatest common divisor, which is 9. Therefore, "36 : 9" simplifies to "4 : 1".

Explanation

The given expression "36 : 9" can be simplified by dividing both numbers by their greatest common divisor, which is 9. Therefore, "36 : 9" simplifies to "4 : 1".

10) What Is 0.2 x 0.3?

0.05

0.5

0.6

0.06

The correct answer is 0.06 because when you multiply 0.2 by 0.3, you get the product of 0.06.

Explanation

The correct answer is 0.06 because when you multiply 0.2 by 0.3, you get the product of 0.06.

11) 0.2 + 0.5 + ... =

The sum of the series 0.2 + 0.5 + ... is equal to 0.3 or 3/10. This can be determined by recognizing that each term in the series is increasing by 0.3, and the sum of an infinite geometric series can be calculated using the formula S = a / (1 - r), where a is the first term and r is the common ratio. In this case, a = 0.2 and r = 0.5. Plugging these values into the formula gives S = 0.2 / (1 - 0.5) = 0.2 / 0.5 = 0.4. Therefore, the sum of the series is 0.4, which is equal to 0.3 or 3/10.

Explanation

The sum of the series 0.2 + 0.5 + ... is equal to 0.3 or 3/10. This can be determined by recognizing that each term in the series is increasing by 0.3, and the sum of an infinite geometric series can be calculated using the formula S = a / (1 - r), where a is the first term and r is the common ratio. In this case, a = 0.2 and r = 0.5. Plugging these values into the formula gives S = 0.2 / (1 - 0.5) = 0.2 / 0.5 = 0.4. Therefore, the sum of the series is 0.4, which is equal to 0.3 or 3/10.

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