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GCSE Foundation 1-Mark Wonders

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Number
Value of a digit
\[ \text{Value of 7 in } 3.472 \]
Use place value: what is the digit worth?
Words to figures
\[ \text{Forty thousand and six} \]
Write the number, using zeros to hold empty places.
Read a scale
\[ \text{Reading on the scale} \]
Work out what each small space is worth first.
Spot a square or cube number
\[ \text{Cube: } 9, 27, 36? \]
Squares: n × n. Cubes: n × n × n.
Square root between two integers
\[ 7 < \sqrt{50} < 8 \]
Find the square numbers either side.
Reciprocal
\[ \text{Reciprocal of } \frac{3}{4} \]
The reciprocal is 1 divided by the number.
Index notation and zero power
\[ 3 \times 3 \times 3 \times 3 = 3^4 \]
The power counts how many are multiplied.
Write in standard form
\[ 46\,000 = 4.6 \times 10^4 \]
A number from 1 to 10, times a power of 10.
Standard form to ordinary number
\[ 3.7 \times 10^{-3} \]
The power tells you how far the digits move.
Round to 2 or 3 s.f.
\[ 0.04067 \to 2 \text{ s.f.} \]
Count from the first non-zero digit.
Fractions, percentages and ratio
Simplify a fraction
\[ \frac{18}{24} = \frac{3}{4} \]
Divide top and bottom by the highest common factor.
Improper fraction and mixed number
\[ \frac{17}{5} = 3\frac{2}{5} \]
How many wholes, and what is left over?
Decimal to percentage
\[ 0.035 = 3.5\% \]
Multiply by 100.
Percentage to fraction
\[ 35\% = \frac{7}{20} \]
Write it over 100, then simplify.
Ratio in the form 1 : n
\[ 4 : 10 = 1 : 2.5 \]
Divide both parts by the first number.
Algebra and graphs
Expression, equation, formula or identity
\[ 3x + 2 = 11 \]
Look for =, ≡ and how many letters there are.
Write an expression
\[ \text{5 less than } x \]
Turn the words into algebra, in the right order.
Next term of a sequence
\[ 3, 6, 12, 24, \ldots \]
Look at the differences, or what you multiply by.
Inequality from a number line
\[ -2 \le x < 3 \]
Filled circle: included. Empty circle: not.
Midpoint of two points
\[ (2, 4), (6, 10) \]
Add the coordinates and halve.
Horizontal and vertical lines
\[ x = 3 \text{ or } y = 3? \]
x = a number is vertical; y = a number is horizontal.
Shape and angles
Types of angle
\[ 205^\circ \to \text{reflex} \]
Acute, right, obtuse or reflex?
Name a shape from its properties
\[ \text{One pair of parallel sides} \]
Check sides, angles and parallel lines.
Faces, edges and vertices
\[ \text{Edges: triangular prism} \]
Count the hidden ones too.
Lines or order of symmetry
\[ \text{Lines of symmetry} \]
Fold it, or turn it with tracing paper.
Angles in polygons
\[ 360^\circ \div 8 = 45^\circ \]
Exterior angles add up to 360°.
Back bearings
\[ 070^\circ \to 250^\circ \]
Add or subtract 180°; use three figures.
Measures, transformations and vectors
Time: hours and minutes
\[ 2.5 \text{ h} = 150 \text{ min} \]
There are 60 minutes in an hour, not 100.
Reflect a point
\[ (3, -2) \text{ in the } y\text{-axis} \]
Same distance from the mirror line, on the other side.
Translation vector
\[ \text{Translation } A \to B \]
Across on top, up or down underneath.
Column vectors
\[ 2\binom{3}{-1} + \binom{-4}{5} \]
Work on the top numbers and the bottom numbers.
Statistics and probability
Read a bar chart
\[ \text{Frequency for Tuesday} \]
Read the scale before reading the bar.
Read a pictogram
\[ \text{Key: } \bullet = 4 \]
Use the key, and value part symbols carefully.
Pie chart angles
\[ 90^\circ = 32 \text{ people} \]
The whole circle, 360°, is everyone.
Type of correlation
\[ \text{Positive, negative or none?} \]
Positive, negative or none?
Types of data
\[ \text{Shoe size: discrete} \]
Qualitative, discrete or continuous?
Mode from a frequency table
\[ \text{Modal number of pets} \]
The value with the biggest frequency.
Probability words and scale
\[ P = 0.75 \to \text{likely} \]
From 0 (impossible) to 1 (certain).
Expected frequency
\[ 0.15 \times 200 = 30 \]
Probability × number of trials.
Count combinations
\[ 3 \times 5 = 15 \text{ meals} \]
Multiply the numbers of choices.
Calculator questions
Calculator: powers and roots
\[ \sqrt[3]{90} \to 3 \text{ s.f.} \]
Use the right key, then round as asked.
Calculator: the fraction bar
\[ \frac{8.4 + 3.17}{2.6 \times 1.9} \]
Top and bottom are each in brackets.
Calculator: negatives and powers
\[ (-4.3)^2 – 6.1 \]
Put the negative number in brackets.
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