0:00

GCSE Higher 1-Mark Wonders

Select the skills to practise, and then click Go!

Number and proportion
Reciprocal
\[ \text{Reciprocal of } 2\tfrac{1}{2} \]
Write it as a fraction, then turn it upside down.
Write as a power
\[ \tfrac{1}{81} = 3^{n} \]
Roots are fractional powers; 1 over is a negative power.
Rational or irrational?
\[ \sqrt{18} \to \text{irrational} \]
Can it be written as a fraction of whole numbers?
Write in standard form
\[ 32 \times 10^5 = 3.2 \times 10^6 \]
The first number must be from 1 up to 10.
Standard form to ordinary number
\[ 4.07 \times 10^{-4} \]
The power tells you how far the digits move.
Fraction to recurring decimal
\[ \tfrac{5}{11} = 0.\dot{4}\dot{5} \]
Divide, then dot the first and last repeating digit.
Error interval: truncation
\[ 6.4 \le x < 6.5 \]
Truncating chops digits off; it never rounds up.
Percentage multipliers
\[ \text{Down } 4\% \to \times 0.96 \]
Add to or take away from 100%, then divide by 100.
Proportion: effect of a change
\[ y \propto x^2,\ x \times 3 \]
Put the new x into the rule.
Algebra and graphs
Type of sequence
\[ 2, 6, 18, 54 \to \text{geometric} \]
Check differences, ratios and the two terms before.
Common ratio
\[ 48, 12, 3, \ldots \to \tfrac{1}{4} \]
Divide a term by the one before it.
Gradient from ax + by = c
\[ 3x + 2y = 7 \to m = -\tfrac{3}{2} \]
Get y on its own first.
Inequality from a number line
\[ x < -1 \text{ or } x \ge 3 \]
Filled circle: included. Two parts: use “or”.
Roots from a graph
\[ \text{Roots of } y = f(x) \]
Where does the curve cross the x-axis?
Match a graph to its equation
\[ \text{Sketch} \to y = \tfrac{1}{x} \]
Know the shapes of the key graphs.
Motion graphs: gradient or area
\[ \text{v–t gradient} \to \text{acceleration} \]
Gradient gives speed or acceleration; area gives distance.
Circle x² + y² = r²
\[ x^2 + y^2 = 49 \to r = 7 \]
The number on the right is the radius squared.
Transform a point on y = f(x)
\[ (2, 5) \to y = f(x + 3) \]
Inside the bracket: x moves the opposite way.
Graph translation as a vector
\[ y = f(x – 2) + 1 \]
f(x − a) + b moves by a across and b up.
Geometry and measures
Vectors in a shape
\[ \overrightarrow{AB} = \mathbf{b} – \mathbf{a} \]
Find a route along known vectors; watch the direction.
Invariant point
\[ \text{Reflect in } y = x \]
An invariant point does not move.
Congruence condition
\[ \text{SSS, SAS, ASA or RHS?} \]
SSS, SAS, ASA or RHS: what is marked equal?
Area units
\[ 3.5\text{m}^2 = \square\text{cm}^2 \]
Square the length conversion.
Volume units
\[ 0.2\text{m}^3 = \square\text{cm}^3 \]
Cube the length conversion.
Statistics and probability
Identify the outlier
\[ \text{Outlier on the scatter} \]
Find the point far from the trend; x first.
Read a box plot
\[ \text{IQR from a box plot} \]
Box ends are the quartiles; the line is the median.
Class containing the median
\[ \text{Median of 60 values} \]
Find the middle position, then a running total.
Set notation from a Venn diagram
\[ A \cap B’ = \{2, 8\} \]
∩ is AND, ∪ is OR, a dash means NOT.
Product rule for counting
\[ \text{4-digit codes, no repeats} \]
Multiply the numbers of choices.
Calculator questions
Calculator: fraction bar, roots and powers
\[ \tfrac{\sqrt{19.4}}{2.3^2 – 1.7} \]
Brackets round the top, the bottom and under roots.
Calculator: standard form
\[ \tfrac{3.2 \times 10^5}{6.4 \times 10^{-3}} \]
Use the ×10ˣ key; answer in standard form.
Calculator: negative and fractional powers
\[ 17^{\frac{2}{5}} \to 3 \text{ s.f.} \]
Put a fractional power in brackets.
Timer (Optional)
No skills selected
Question