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3.2H Fractions: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Simplify the fraction 18/24.

(Total for Question 1 is 1 mark)

Work out 5/6 + 1/3. Give your answer as an improper fraction.

(Total for Question 2 is 2 marks)

Work out 5 1/4 - 2 3/8. Give your answer as an improper fraction.

(Total for Question 3 is 2 marks)

Work out (3/5) x (25/6). Simplify your answer.

(Total for Question 4 is 2 marks)

Work out (7/8) ÷ (3/4). Simplify your answer.

(Total for Question 5 is 3 marks)

Simplify the algebraic expression (2/3)x - (1/6)x.

(Total for Question 6 is 2 marks)

a) Show that 1/(1 + a) + 1/(1 - a) = 2/(1 - a²).
b) Hence or otherwise, find the value of the expression when a = 1/3.

(a)Show that 1/(1 + a) + 1/(1 - a) = 2/(1 - a²).(3)

(b)Find the value when a = 1/3.(1)

(Total for Question 7 is 4 marks)

A recipe requires 2/3 cup of sugar for one batch of cookies. Olivia has 5 1/2 cups of sugar. What is the maximum number of full batches she can make?

(Total for Question 8 is 2 marks)

Solve the equation (2x + 1)/3 - (x - 2)/4 = 5/6. Give your answer as a fraction or integer.

(Total for Question 9 is 3 marks)

Mark scheme · 3.2H Fractions: Higher Tier Practice

Question 1

B1 3/4 cao
Answer: 3/4

Question 2

M1 common denominator 6, 5/6 + 2/6 or equivalent method
A1 7/6 cao
Answer: 7/6

Question 3

M1 convert to improper fractions or use common denominator: 21/4 - 19/8 or equivalent
A1 23/8 cao
Answer: 23/8

Question 4

M1 multiply numerators and denominators or cancel then multiply, e.g. 3*25 / 5*6 oe
A1 5/2 cao
Answer: 5/2

Question 5

M1 use reciprocal: (7/8) * (4/3) or equivalent
M1 multiply to get 28/24 or show cancellation 7*4 / 8*3
A1 7/6 cao
Answer: 7/6

Question 6

M1 find common coefficients: 4/6 x - 1/6 x or equivalent
A1 1/2 x cao
Answer: 1/2 x

Question 7

(a) M1 write common denominator (1+a)(1-a) and combine numerators, e.g. (1-a + 1+a)/(1-a²) or equivalent
(a) M1 simplify numerator to 2
(a) A1 2/(1-a²) cao (cso)
(a) Answer: 2/(1-a²)
(b) B1 9/4 cao
(b) Answer: 9/4

Question 8

M1 divide 5.5 by 2/3 or equivalent: 5 1/2 * 3/2
A1 8 cao
Answer: 8

Question 9

M1 clear denominators by multiplying by 12 to get 4(2x+1) - 3(x-2) = 10 or equivalent
M1 collect terms: 8x+4 -3x+6 = 10 => 5x +10 =10
A1 x = 0 cao
Answer: 0

Fractions: Higher Tier Practice - Worksheets, Questions and Revision