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Higher 1-Mark Skills
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Indices and Powers
Evaluate power of zero
\[ 7^0 = 1 \]
Any non-zero number to power 0 equals 1.
Evaluate negative indices
\[ 2^{-3} = \frac{1}{8} \]
Express as a unit fraction.
Fractional index (square root)
\[ 49^{\frac{1}{2}} = 7 \]
Index 1/2 means square root.
Fractional index (cube root)
\[ 125^{\frac{1}{3}} = 5 \]
Index 1/3 means cube root.
Combined fractional indices
\[ 8^{\frac{2}{3}} = 4 \]
Root first, then power.
Find reciprocals
\[ \text{Reciprocal of } 0.4 = 2.5 \]
Reciprocal = 1 ÷ number.
Standard Form
Convert to standard form
\[ 468000 = 4.68 \times 10^5 \]
Write as A × 10ⁿ where 1 ≤ A < 10.
Convert to ordinary number
\[ 3.7 \times 10^{-4} = 0.00037 \]
Convert from standard form.
Bounds and Error Intervals
Error interval (rounded)
\[ 9.35 \leq x < 9.45 \]
Find bounds for a rounded number.
Error interval (truncated)
\[ 6.4 \leq x < 6.5 \]
Find bounds for a truncated number.
Recurring Decimals
Fraction to recurring decimal
\[ \frac{2}{9} = 0.\dot{2} \]
Use dot notation for recurring decimals.
Equations of Lines
Find gradient from equation
\[ y = -4x + 7 \rightarrow m = -4 \]
Coefficient of x is the gradient.
Find y-intercept
\[ y = 3x – 5 \rightarrow (0, -5) \]
Where the line crosses the y-axis.
Perpendicular gradient
\[ m = 3 \rightarrow m_\perp = -\frac{1}{3} \]
Negative reciprocal.
Parallel gradient
\[ \text{Parallel lines: same } m \]
Parallel lines have equal gradients.
Interpreting Graphs
Turning point from completed square
\[ (x-3)^2 + 5 \rightarrow (3, 5) \]
Read coordinates from vertex form.
Match equation to graph type
\[ y = \frac{k}{x} \rightarrow \text{reciprocal} \]
Identify function from graph shape.
Interpret motion graphs
\[ \text{Gradient, Area, Features} \]
Velocity-time and distance-time graphs.
Inequalities
Inequality from number line
\[ -2 \leq x < 3 \]
Read inequality from diagram.
Exact Trigonometry
Exact trig values
\[ \sin, \cos, \tan \text{ of } 0°, 30°, 45°, 60°, 90° \]
Memorise standard angles.
Vectors
Vector addition/subtraction
\[ \mathbf{a} + \mathbf{b} \]
Add/subtract components.
Scalar multiplication
\[ 3\begin{pmatrix} 2 \\ -4 \end{pmatrix} = \begin{pmatrix} 6 \\ -12 \end{pmatrix} \]
Multiply each component by scalar.
Combined vector operations
\[ 2\mathbf{a} + \mathbf{b} \]
Scalar multiply then add/subtract.
Transformations
Translation as vector
\[ \begin{pmatrix} 3 \\ -2 \end{pmatrix} \]
Write translation as column vector.
Invariant points
\[ \text{Points on mirror line} \]
Points on reflection line don’t move.
Unit Conversions
Convert area units
\[ 5 \text{ m}^2 = 50000 \text{ cm}^2 \]
Square the linear conversion factor.
Convert volume units
\[ 2 \text{ m}^3 = 2000000 \text{ cm}^3 \]
Cube the linear conversion factor.
Probability
Probability of complement
\[ P(\text{not } A) = 1 – P(A) \]
Complementary events sum to 1.
Read from tree diagram
\[ \text{Read branch probability} \]
Read single probability from branch.
Correlation
Describe correlation
\[ \text{positive / negative / none} \]
Describe type of correlation.
Identify outlier coordinates
\[ \text{Find the point that doesn’t fit} \]
Give coordinates of the outlier.
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