Section A
Multiplying and Dividing by Powers of 10
Method: Write 10², 10³, … as 100, 1000, … and 10⁻¹, 10⁻², … as 1/10, 1/100, … Multiplying by a negative power of 10 is the same as dividing by the positive power; dividing by a negative power is the same as multiplying by the positive power.
Example: 0.45 ÷ 10⁻³ — dividing by 10⁻³ (a thousandth) is the same as multiplying by 1000 → 0.45 × 1000 = 450
Q1
Work out 4.5 × 10²
1 mark
Q2
Work out 7 × 10⁻²
1 mark
Q3
Work out 320 ÷ 10³
1 mark
Q4
Work out 0.06 × 10⁴
1 mark
Q5
When you multiply a positive number by 10 raised to a negative power, the result is always … than the number you started with. Write one word.
1 mark
Q6
Work out 8.5 ÷ 10⁻²
2 marks
Q7
Work out 42 ÷ 10⁻¹
2 marks
POWERS OF 10 — SECTION SCORE
0/9
Section B
Multiplying and Dividing Decimals
Method: Ignore the decimal points, work out the calculation with whole numbers, then place the decimal point back using place value. For division, multiply the top and bottom of the calculation by 10, 100, … to make an equivalent calculation with whole numbers, which is easier to do.
Example: −16 ÷ 0.4 → multiply top and bottom by 10 → −160 ÷ 4 = −40
Q8
Work out 12 × 0.4
1 mark
Q9
Work out 0.3 × 0.15
1 mark
Q10
Work out 0.8 ÷ 0.02
1 mark
Q11
Work out −16 ÷ 0.4
2 marks
Q12
Work out 4.5 ÷ 0.5
1 mark
Q13
Work out (36 × 0.5) ÷ (0.2 × 4.5)
2 marks
Q14
0.23 × 37.8 is closest to which of these values?
1 mark
DECIMAL CALCULATIONS — SECTION SCORE
0/9
Section C
Compound Percentages
Method: Turn each percentage change into a multiplier (add the percentage to 100% for an increase, subtract it from 100% for a decrease, then divide by 100), and apply the multipliers one after another, in order. Repeating the same multiplier n times can be written using a power: ×(multiplier)ⁿ.
Example: $12000 decreased by 20%, then by a further 15% → 12000 × 0.8 × 0.85 = $8160
Q15
A price of $250 is increased by 20%, then the new price is decreased by 10%. Work out the final price, in dollars.
2 marks
Q16
Write the multiplier that represents a 15% decrease.
1 mark
Q17
$400 is increased by 10%, then increased by a further 10%. Work out the final value, in dollars.
2 marks
Q18
A value is increased by 20%, then decreased by 20%. Does it end up higher, lower, or the same as the original value? Write one word.
1 mark
Q19
$2000 is invested at 5% interest per year, compounded annually. Work out the value of the investment after 3 years, to the nearest dollar.
2 marks
Q20
Which calculation gives the value of $600 after two successive 8% decreases?
1 mark
Q21
A car bought for $18000 loses 15% of its value in the first year, then loses a further 10% of its new value in the second year. Work out its value at the end of the second year, in dollars.
2 marks
Q22
A town's population is 8000, and is predicted to fall by 5% each year. Which calculation gives the population after 4 years?
1 mark
COMPOUND PERCENTAGES — SECTION SCORE
0/12
Section D
Upper and Lower Bounds
Method: A rounded value could have come from a range of exact values. For a measurement (length, mass, time), the lower bound is half a unit of rounding below the rounded value and the upper bound is half a unit of rounding above it, written as an inequality: lower bound ≤ exact value < upper bound. For a count of whole things (people, cars), the exact value must be a whole number, so the upper bound is the largest whole number that still rounds to the given value.
Example: A crowd of 104000, correct to the nearest 1000 → lower bound = 103500, upper bound = 104499 (there cannot be half a person). A length of 104 m, correct to the nearest m → 103.5 ≤ x < 104.5.
Q23
A length is measured as 40 cm, correct to the nearest cm. Write the lower bound of the length.
1 mark
cm
Q24
Using the same length (40 cm, correct to the nearest cm), write the upper bound of the length.
1 mark
cm
Q25
A number is rounded to the nearest 100. The answer is 300. Which inequality correctly shows the range of the original number?
1 mark
Q26
The mass of a bag of rice is given as 2.4 kg, correct to 1 decimal place. Write the upper bound of the mass.
2 marks
kg
Q27
The area of a field is given as 1560 m², correct to the nearest 10 m². Which inequality shows the range of possible exact areas?
2 marks
Q28
A stack of 50 identical coins has a height of 40 mm, correct to the nearest mm. Using the lower bound of the stack's height, work out the smallest possible height of a single coin, in mm.
2 marks
mm
Q29
A decimal number, which could have any number of decimal places, is rounded to the nearest whole number, giving 12. Write the correct upper bound.
1 mark
BOUNDS — SECTION SCORE
0/10
0%
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