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GCSE Foundation (Calculator)
Select the skills to practice, and then click Go!
Calculator basics
Use BIDMAS with calculator
\[ \frac{9.8 \times 6.8}{4.2 – 2.1} \]
Enter a multi-step calculation correctly.
Write calculator display and round
\[ 47 \div 6 = \text{?} \]
Record full display then round.
Percentage calculations
Percentage of an amount
\[ 17\% \text{ of } £845 \]
Work out a percentage of a given amount.
Percentage increase
\[ £245 + 18\% \]
Increase an amount by a percentage.
Percentage decrease
\[ 680\text{kg} – 23\% \]
Decrease an amount by a percentage.
Reverse percentage
\[ £119 \text{ after } 15\% \text{ off} \]
Find the original value.
Simple interest
\[ P \times r \times t \]
Calculate simple interest earned.
Compound interest
\[ P(1+r)^n \]
Find the final value with compound interest.
Ratio and proportion
Simplify a ratio
\[ 36:48 \rightarrow 3:4 \]
Simplify a ratio to its lowest terms.
Share in ratio (two parts)
\[ £180 \text{ in } 4:5 \]
Divide an amount into two parts.
Share in ratio (three parts)
\[ £360 \text{ in } 2:3:4 \]
Divide an amount into three parts.
Use ratio to find total
\[ 3:7, \text{ green}=84 \]
Find total from one quantity in a ratio.
Write ratio from context
\[ \text{Triple, half} \rightarrow a:b:c \]
Convert word relationships into ratio form.
Algebra (calculator)
Substitute into formula
\[ T = 4m^2 – 11 \]
Substitute a value into a formula.
Substitute two variables
\[ P = 3a + 4b \]
Substitute two values into a formula.
Rearrange formula (one step)
\[ p = 3a – 9 \]
Rearrange using one inverse operation.
Rearrange formula (two steps)
\[ p = \frac{h+5}{3} \]
Rearrange using two inverse operations.
Solve linear equation
\[ 5x + 7 = 32 \]
Solve a two-step equation.
Solve equation with brackets
\[ 3(2x – 5) = 21 \]
Expand brackets then solve.
Speed distance time
Convert compound units
\[ 25 \text{ m/s} \rightarrow \text{km/h} \]
Change between units of speed.
Calculate speed
\[ S = D \div T \]
Work out speed from distance and time.
Calculate distance or time
\[ D = S \times T \]
Work out distance or time.
Multi-stage journey
\[ T_1 + T_2 = \text{?} \]
Total time for journey with different stages.
Convert time units
\[ 215 \text{ min} \rightarrow \text{h:m} \]
Change minutes to hours and minutes.
Circles
Area of a circle
\[ A = \pi r^2 \]
Work out the area of a circle.
Circumference of a circle
\[ C = \pi d \]
Work out the circumference.
Area of semicircle or quarter
\[ A = \frac{\pi r^2}{2} \]
Work out the area of part of a circle.
Pythagoras
Find the hypotenuse
\[ c = \sqrt{a^2 + b^2} \]
Work out the longest side.
Find a shorter side
\[ a = \sqrt{c^2 – b^2} \]
Work out a shorter side.
Trigonometry
Find a side using SOHCAHTOA
\[ \sin \theta = \frac{O}{H} \]
Use sin, cos or tan to find a side.
Find an angle using SOHCAHTOA
\[ \theta = \tan^{-1}\left(\frac{O}{A}\right) \]
Use inverse trig to find an angle.
Statistics
Mean from a list
\[ \bar{x} = \frac{\sum x}{n} \]
Work out the mean of a set of numbers.
Estimated mean from grouped data
\[ \bar{x} = \frac{\sum fx}{\sum f} \]
Estimated mean from a frequency table.
Find median class interval
\[ \frac{n}{2}\text{th value} \]
Identify the class containing the median.
Combined mean from two groups
\[ \bar{x} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1+n_2} \]
Overall mean when groups are combined.
Probability
Calculate combined probability
\[ P(A \cap B) = P(A) \times P(B) \]
Multiply probabilities for independent events.
Find total from probability
\[ \text{Total} = \frac{f}{P} \]
Use probability to find a missing total.
Find missing probability from tree
\[ P + x = 1 \]
Work out a missing probability.
Money and best value
Multi-item purchase
\[ 5 \times £9.50 + 3 \times £30 \]
Work out total cost for several items.
Best value comparison
\[ 4 \text{ for } £18 \text{ vs } 5 \text{ for } £24 \]
Compare prices to find better value.
Timer (Optional)
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