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Calculate. (a) $(6^2 + 5)^3$ (b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$ Write your answer correct to 3 significant figures. - OCR - GCSE Maths - Question 1 - 2021 - Paper 1

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Question 1

Calculate.-(a)-$(6^2-+-5)^3$--(b)-$\sqrt{\frac{8.4^2---1.9^2}{2.5-+-5.7}}$--Write-your-answer-correct-to-3-significant-figures.-OCR-GCSE Maths-Question 1-2021-Paper 1.png

Calculate. (a) $(6^2 + 5)^3$ (b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$ Write your answer correct to 3 significant figures.

Worked Solution & Example Answer:Calculate. (a) $(6^2 + 5)^3$ (b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$ Write your answer correct to 3 significant figures. - OCR - GCSE Maths - Question 1 - 2021 - Paper 1

Step 1

(a) $(6^2 + 5)^3$

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Answer

To solve the expression, start by calculating 626^2:

62=366^2 = 36

Now substitute this value back into the expression:

(36+5)3(36 + 5)^3

Calculate the sum:

36+5=4136 + 5 = 41

Now raise this result to the power of 3:

413=41×41×41=6892141^3 = 41 \times 41 \times 41 = 68921

Therefore, the answer for part (a) is 68921.

Step 2

(b) $\sqrt{\frac{8.4^2 - 1.9^2}{2.5 + 5.7}}$

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Answer

First, calculate 8.428.4^2 and 1.921.9^2:

8.42=70.568.4^2 = 70.56 1.92=3.611.9^2 = 3.61

Now find the difference:

8.42−1.92=70.56−3.61=66.958.4^2 - 1.9^2 = 70.56 - 3.61 = 66.95

Next, calculate the denominator 2.5+5.72.5 + 5.7:

2.5+5.7=8.22.5 + 5.7 = 8.2

Now we can substitute these results into the formula:

66.958.2\sqrt{\frac{66.95}{8.2}}

Calculate the division:

66.958.2≈8.1634\frac{66.95}{8.2} \approx 8.1634

Now take the square root:

8.1634≈2.857\sqrt{8.1634} \approx 2.857

Finally, round to 3 significant figures:

The answer for part (b) is approximately 2.86.

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