Photo AI

7 (a) Work out - OCR - GCSE Maths - Question 7 - 2023 - Paper 1

Question icon

Question 7

7--(a)-Work-out-OCR-GCSE Maths-Question 7-2023-Paper 1.png

7 (a) Work out. (i) $3^5$ (ii) $\sqrt{2744}$ (b) Find the value of $y$. $384 = 6 \times 4^y$ (c) Write $3^{-1}$ as a fraction.

Worked Solution & Example Answer:7 (a) Work out - OCR - GCSE Maths - Question 7 - 2023 - Paper 1

Step 1

(a)(i) Work out.

96%

114 rated

Answer

To calculate 353^5, we multiply 3 by itself five times:

35=3×3×3×3×3=243.3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243.

Step 2

(a)(ii) Work out.

99%

104 rated

Answer

To find 2744\sqrt{2744}, we need to determine the number whose square gives 2744. We can factor 2744 into primes:

2744 = 2^3 \times 7^3.

Thus, taking the square root:

2744=(23)⋅(73)=23/2⋅73/2=22⋅77=1414.\sqrt{2744} = \sqrt{(2^3)\cdot(7^3)} = 2^{3/2} \cdot 7^{3/2} = 2 \sqrt{2} \cdot 7\sqrt{7} = 14 \sqrt{14}.

Step 3

(b) Find the value of y.

96%

101 rated

Answer

From the equation 384=6×4y384 = 6 \times 4^y, we start by simplifying:

  1. Divide both sides by 6: 3846=64=4y.\frac{384}{6} = 64 = 4^y.
  2. Since 43=644^3 = 64, we find that y=3.y = 3.

Step 4

(c) Write 3^{-1} as a fraction.

98%

120 rated

Answer

The expression 3−13^{-1} represents the reciprocal of 3. Therefore:

3−1=13.3^{-1} = \frac{1}{3}.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;