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Year 8 Essential Skills
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Ratio and Proportion
Simplify a ratio
\[ 24:36 \rightarrow 2:3 \]
Simplify a ratio by dividing by the HCF.
Divide in a ratio
\[ \text{£}45 \text{ in } 2:3 \]
Share a quantity in a given ratio.
Ratio in form 1:n
\[ 4:5 \rightarrow 1:1.25 \]
Express a ratio in the form 1:n.
Fractions
Multiply fractions
\[ \frac{2}{3} \times \frac{3}{4} \]
Multiply two proper fractions.
Divide fraction by integer
\[ \frac{3}{4} \div 2 \]
Divide a fraction by a whole number.
Divide integer by fraction
\[ 6 \div \frac{2}{3} \]
Divide a whole number by a fraction.
Percentages
Percentage of amount
\[ 15\% \text{ of } 80 \]
Find a percentage of an amount mentally.
Percentage increase/decrease
\[ \text{Increase } 60 \text{ by } 20\% \]
Increase or decrease by a percentage.
One number as % of another
\[ 18 \text{ as } \% \text{ of } 60 \]
Express one number as a percentage of another.
Algebra: Expressions
Expand single bracket
\[ 3(2x + 5) \]
Multiply out a single bracket.
Factorise into single bracket
\[ 6x + 9 = 3(…) \]
Take out the HCF as a single bracket.
Simplify with indices
\[ x^3 \times x^4 \]
Use index laws to simplify.
Algebra: Equations
One-step equation
\[ x + 7 = 12 \]
Solve a simple one-step equation.
Two-step equation
\[ 3x + 4 = 19 \]
Solve an equation requiring two steps.
Equation with brackets
\[ 2(x + 3) = 14 \]
Solve an equation by expanding first.
Linear inequality
\[ 3x + 2 < 14 \]
Solve a simple linear inequality.
Sequences
Next term of sequence
\[ 3, 7, 11, 15, … \]
Find the next term of an arithmetic sequence.
Term from nth term
\[ 3n + 2: \text{ 5th term?} \]
Find a specific term using the nth term rule.
Find the nth term
\[ 5, 8, 11, 14, … \]
Find the nth term rule of a sequence.
Indices and Powers
Evaluate a power
\[ 2^5 \]
Calculate a number raised to a power.
Convert to standard form
\[ 4500000 \rightarrow ? \]
Write a large number in standard form.
Standard form to ordinary
\[ 3.5 \times 10^4 \rightarrow ? \]
Convert from standard form to ordinary number.
Coordinates
Write coordinates
\[ \text{Read from grid} \]
Write coordinates from a grid.
Find the midpoint
\[ (2,4) \text{ and } (8,10) \]
Find the midpoint of two coordinates.
Angles
Angles on a straight line
\[ 65° + x° = 180° \]
Find a missing angle on a straight line.
Interior angles of polygon
\[ \text{Regular hexagon} \]
Find the interior angle of a regular polygon.
Area
Area of trapezium
\[ A = \frac{1}{2}(a+b)h \]
Calculate the area of a trapezium.
Area of circle (in terms of π)
\[ A = \pi r^2 \]
Find the area of a circle with radius given.
Probability
Probability from outcomes
\[ P(\text{blue}) = ? \]
Calculate probability from a list of outcomes.
Probability from two-way table
\[ P(\text{male and tea}) \]
Calculate probability from a two-way table.
Statistics
Calculate the mean
\[ \text{Mean of } 4, 7, 3, 8, 3 \]
Find the mean of a list of numbers.
Find the median
\[ \text{Median of } 3, 8, 2, 9, 4 \]
Find the median from an unordered list.
Calculate the range
\[ \text{Range of } 5, 12, 3, 18, 7 \]
Find the range of a set of numbers.
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