MATHS HIGHER TOPIC NUMBER

Prime factorisation of 840

2³ × 3 × 5 × 7.

HCF of 84 and 126

42.

LCM of 84 and 126

252.

HCF of 180 and 252

36.

LCM of 45 and 72

360.

0.375 as a fraction

3/8.

2 3/5 as an improper fraction

13/5.

Calculate 3/4 + 5/6

19/12.

Calculate 7/8 ÷ 14/15

15/16.

0.625 as a fraction

5/8.

0.00072 in standard form

7.2 × 10⁻⁴.

5.63 × 10⁵ as an ordinary number

563,000.

(3 × 10⁵)(4 × 10⁻³) in standard form

1.2 × 10³.

(8.4 × 10⁷) ÷ (2.1 × 10³) in standard form

4 × 10⁴.

3.2 × 10⁵ + 4.5 × 10⁴ in standard form

3.65 × 10⁵.

Simplify 2³ × 2⁵

2⁸ = 256.

Simplify x⁷ ÷ x³

x⁴.

Simplify (a³)⁴

a¹².

Simplify 5⁻²

1/25.

Evaluate 27^(2/3)

9.

Evaluate 16^(3/4)

8.

Simplify √72

6√2.

Simplify √200

10√2.

Simplify 3√5 + 7√5

10√5.

Simplify 4√3 × 2√6

24√2.

Rationalise the denominator of 5/√3

5√3/3.

Rationalise the denominator of 3/(2√5)

3√5/10.

1/3 as a recurring decimal

0.333…

2/11 as a recurring decimal

0.181818…

Convert 0.777… into a fraction

7/9.

Convert 0.272727… into a fraction

3/11.

Is √49 rational or irrational?

Rational, because √49 = 7.

Is √50 rational or irrational?

Irrational, because √50 = 5√2 and √2 is irrational.

Irrational numbers among √16, √18, π, 0.25

√18 and π.

Round 7.8462 to 2 decimal places

7.85.

Round 0.004738 to 2 significant figures

0.0047.

Round 58,739 to 3 significant figures

58,700.

Round 0.09648 to 3 significant figures

0.0965.

Estimate (49.7 × 21.2) ÷ 9.8 using 1 significant figure

Approximately 100.

Estimate √48 + 6.1²

Approximately 15.

Error interval for length 7.4 cm nearest 0.1 cm

7.35 ≤ x < 7.45.

Error interval for mass 250 g nearest 10 g

245 ≤ x < 255 g.

Upper and lower bounds for length 12 cm nearest cm

Lower = 11.5 cm, upper = 12.5 cm.

Error interval for value rounded to 3 significant figures to 4.52

4.515 ≤ x < 4.525.

Error interval for number rounded to nearest 100 becomes 3600

3550 ≤ x < 3650.

Maximum possible area of rectangle 8 cm by 5 cm both rounded

8.5 × 5.5 = 46.75 cm².

Minimum possible area of rectangle 8 cm by 5 cm both rounded

7.5 × 4.5 = 33.75 cm².

Percentage increase from £80 to £92

15%.

Percentage decrease from £250 to £200

20%.

Multiplier for a number increased by 15%

1.15.

Multiplier for a number decreased by 28%

0.72.

New price after reducing £80 jacket by 35%

£52.

New population from 12,000 increased by 8%

12,960.

Expression for investment increasing 4% yearly after 5 years from £3000

3000 × 1.04⁵.

Car value after 3 years decreasing by 12% from £20,000

£13,655.36.

Is a quantity back to original value after 10% increase and decrease?

No, it's 1% lower.

Percentage increase from 40,000 to 46,000

15%.

Original value from 90 after 25% increase

72.

Original price from £64 after 20% reduction

£80.

Percentage change from £5000 to £5600

12% increase.

Reciprocal of 7

1/7.

Reciprocal of 3/5

5/3.

Reciprocal of 2√3

√3/6.

Calculate 1/2 + 1/3 + 1/6

1.

Calculate 2 1/4 × 1 1/3

3.

Calculate 5/6 − 7/12

1/4.

Smallest number divisible by both 6 and 15

30.

Smallest number divisible by 8 and 12

24.

Number of factors of n with prime factorisation 2⁴ × 3² × 5

30.

Number of factors of n with prime factorisation 2³ × 5²

12.

Smallest number to multiply by 180 to make perfect square

5.

Smallest number to multiply by 540 to make perfect cube

50.

Largest square number factor of 1800

900.

Smallest square number multiple of 72

144.

Number between 40 and 50 divisible by both 3 and 5

45.

Type of number with exactly 3 factors

Square of a prime number.

Prove square of any odd integer is odd

Let it be 2n + 1; its square is odd.

Prove the sum of two odd numbers is even

Let them be 2a + 1 and 2b + 1; their sum is even.

Maximum possible percentage error for rounded 3.47 to 2 decimal places

Approximately 0.144%.

Maximum absolute error for measurement 50 cm nearest cm

0.5 cm.

Maximum percentage error for measurement 50 cm nearest cm

1%.

Times larger is 7.2 × 10⁻³ than 3.6 × 10⁻⁵

200 times.

How many times heavier is Earth than object of 1.99 × 10²² kg

300 times.

Simplify √8 + √18

5√2.

Simplify (√5 + 2)(√5 − 2)

1.

Simplify (3 + √2)(3 − √2)

7.

If x = √3, find x² + 2x

3 + 2√3.

Rationalise denominator of surd expression 1/(√3 + 1)

(√3 − 1)/2.

Express 0.125 as a fraction and percentage

1/8 and 12.5%.

Express 7/20 as a decimal and percentage

0.35 and 35%.

Overall percentage increase from increases of 12% and 8%

20.96%.

Overall percentage decrease from decreases of 15% and 20%

32%.

Percentage of original population remaining after 4 years with 6% decrease

Approximately 78.07%.

Multiplier after 12 years for value doubling every 3 years

16.

Original price from £126 at 30% discount

£180.

Original price from £240 after 20% increase

£200.

Smaller number if larger number is 84 and 40% greater

60.