2. (a) Simplify fully - OCR - GCSE Maths - Question 2 - 2019 - Paper 5
Question 2
2. (a) Simplify fully.
\[ \frac{3a^8 \times 2a^5}{a^2} \]
(b) Solve.
\[ \frac{6x - 10}{5} = 1 \]
Worked Solution & Example Answer:2. (a) Simplify fully - OCR - GCSE Maths - Question 2 - 2019 - Paper 5
(a) Simplify fully.
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To simplify the expression ( \frac{3a^8 \times 2a^5}{a^2} ), we can begin by simplifying the numerator.
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Multiply the terms in the numerator:
[ 3a^8 \times 2a^5 = 6a^{8+5} = 6a^{13} ]
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Now the expression becomes:
[ \frac{6a^{13}}{a^2} ]
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Use the laws of exponents to simplify further:
[ \frac{6a^{13}}{a^{2}} = 6a^{13-2} = 6a^{11} ]
Thus, the simplified expression is 6a^{11}.
(b) Solve.
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To solve the equation ( \frac{6x - 10}{5} = 1 ):
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Multiply both sides by 5 to eliminate the fraction:
[ 6x - 10 = 5 ]
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Add 10 to both sides:
[ 6x = 15 ]
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Divide by 6 to isolate ( x ):
[ x = \frac{15}{6} = \frac{5}{2} ]
The solution is x = \frac{5}{2}.
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