Exam Practice 1
EXAM PRACTICE: NUMBER 1
Give all answers where appropriate as fractions or mixed numbers in their lowest terms.
1. Simplify:
a) 14/42
b) 140/42
c) 1.4/42
2. Calculate:
a) 5/12 × 5
b) 1 7/8 ÷ 1 4/5
3. Calculate:
4 1/9 + 3 1/12 – 1 1/4
4. Calculate:
a) 3 + 2 × (1 + 4)2
b) 1/2 + 1/2 ÷ 5/6
5. A recent survey has found that the Great Wall of China is more than twice as long as was previously thought. Its length is now given as 21,196.18 km. Write this length:
a) Correct to 1 d.p.
b) Correct to 1 s.f.
6. The planning rules for a housing development state that:
1/3 of the houses should have three bedrooms, 3/8 should have four bedrooms, 1/24 should be executive homes, and the rest should have two bedrooms.
a) What fraction of the houses have two bedrooms?
b) If 24 houses have two bedrooms, how many houses are on the development?
7. Olivia’s fish tank contains 42 2/3 litres of water. She is emptying it out using a scoop which holds 1 1/3 litres of water. How many full scoops will it take to empty the tank?
Total: 25 marks
The Summary
CHAPTER SUMMARY: NUMBER 1
WORKING WITH FRACTIONS
Always simplify fractions to their lowest terms: 46 = 23
The word ‘of’ means the same as ‘multiplied by’: 12 of 13 = 16
Convert mixed numbers into improper fractions: 149 = 139
Treat whole numbers as fractions, e.g., 5 = 51
To divide by a fraction, turn the fraction upside down and multiply: 12 ÷ 13 = 12 × 31 = 32
To add or subtract fractions, put them over a common denominator: 14 − 16 = 112
ORDER OF OPERATIONS (BIDMAS)
- First B Brackets
- Second I Indices
- Third DM Division and/or Multiplication, working from left to right
- Fourth AS Addition and/or Subtraction, working from left to right
The part of the expression being worked out at each step is highlighted in yellow.
5 + (2 + 1)2 × 4 = 5 + 32 × 4 Brackets
5 + 32 × 4 = 5 + 9 × 4 Indices
5 + 9 × 4 = 5 + 36 Division and/or Multiplication
5 + 36 = 41 Addition and/or Subtraction
Note that calculators use the correct order of operations.
SIGNIFICANT FIGURES AND DECIMAL PLACES
The first significant figure is the first non-zero digit in the number, counting from the left.
The first s.f. is highlighted in yellow.
a) 3400 b) 0.367 c) 0.00845
For decimal places, count after the decimal point (going from left to right).
The third d.p. is highlighted in yellow.
a) 12.3456 b) 0.00073
For example, when rounding to 2 s.f., look at the third s.f. If this is greater than or equal to 5, then round the second figure up. If rounding to 3 s.f., look at the fourth s.f. and so on.
2499 = 2000 (1 s.f.), 2499 = 2500 (2 s.f.), 0.2499 = 0.2 (1 d.p.), 0.2499 = 0.25 (2 d.p.)
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