GCSE Foundation and Higher Mathematics Revision

Comprehensive practice flashcards reviewing core mathematics topics including geometry, trigonometry, percentages, indices, straight line equations, fractions, decimals, and metric conversions.

Area of a Triangle

$$\frac{\text{base} \times\text{height}}{2}$$

Area of a Rectangle

$$\text{base}\times\text{height}$$

What is the formula for calculating the area of a trapezium?

$\text{Area} = \frac{1}{2}(a + b)h$ (or $\frac{(a + b)h}{2}$)

What is the formula for the area of a circle?

$$\text{Area} = \pi r^2$$

What is the formula for calculating the area of a sector of a circle?

$$\text{Area} = \frac{\theta}{360} \times \pi r^2$$

What is the formula for the circumference of a circle?

$$\text{Circumference} = \pi d$$

What is the formula for finding the length of an arc (section of the circumference)?

$$\text{Arc length} = \frac{\theta}{360} \times \pi d$$

What is the formula for Pythagoras' theorem in a right-angled triangle?

$$a^2 + b^2 = c^2$$

What is the general formula to find the volume of a 3D prism?

$$\text{Volume} = \text{area of cross section} \times \text{width}$$

What is the formula for the volume of a cylinder?

$$\text{Volume} = \pi r^2 \times w$$

What relationship does the mnemonic "Don't Shoot Teddy" represent?

Distance, Speed, and Time: $\text{Distance} = \text{Speed} \times \text{Time}$ ($D = S \times T$)

What relationship does the mnemonic "My Dads Van" represent?

Mass, Density, and Volume: $\text{Mass} = \text{Density} \times \text{Volume}$ ($M = D \times V$)

What is the formula for the sum of the interior angles of a polygon with $n$ sides?

$$\text{Sum of interior angles} = (n - 2) \times 180^\circ$$

How do you calculate the size of one interior angle in a regular 6-sided hexagon?

Calculate the total interior sum $(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$, then divide by the number of sides: $720^\circ \div 6 = 120^\circ$.

What is the formula to calculate each exterior angle of a regular polygon with $n$ sides?

$$\text{Exterior angle} = 360^\circ \div n$$

What do all exterior angles of any polygon add up to?

$$360^\circ$$

What is the relationship between an interior angle and its adjacent exterior angle on a straight line?

$$\text{Interior} + \text{exterior} = 180^\circ$$

According to SOH CAH TOA, what are the rearranged formulas for finding the Opposite side ($O$), Adjacent side ($A$), and Hypotenuse ($H$)?

$O = \sin(\theta) \times H$, $A = \cos(\theta) \times H$, and $O = \tan(\theta) \times A$ (with $H = \frac{O}{\sin(\theta)}$, $H = \frac{A}{\cos(\theta)}$, and $A = \frac{O}{\tan(\theta)}$)

What inverse trigonometric functions are used to calculate the angle $\theta$?

$\sin^{-1}\left(\frac{O}{H}\right)$, $\cos^{-1}\left(\frac{A}{H}\right)$, and $\tan^{-1}\left(\frac{O}{A}\right)$

What is the formula for calculating percentage change?

$$\text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100$$

What is the formula for calculating compound interest over a number of years?

$$\text{original} \times \text{multiplier}^{\text{years}} = \text{new}$$

How do you calculate the multiplier for a percentage increase (e.g., a $12\%$ increase)?

Add the percentage to $100\%$ and divide by $100$: $(100 + 12) \div 100 = 112 \div 100 = 1.12$.

How do you calculate the multiplier for a percentage decrease (e.g., a $12\%$ decrease)?

Subtract the percentage from $100\%$ and divide by $100$: $(100 - 12) \div 100 = 88 \div 100 = 0.88$.

What does any non-zero number or term raised to the power of zero equal?

$1$ (e.g., $3^0 = 1$, $x^0 = 1$, $576^0 = 1$, and $(xyz)^0 = 1$)

What is the index law for multiplying terms with the same base (e.g., $x^5 \times x^3$)?

Add the powers: $x^a \times x^b = x^{a+b}$ (e.g., $x^5 \times x^3 = x^{5+3} = x^8$).

What is the index law for dividing terms with the same base (e.g., $\frac{x^{10}}{x^2}$)?

Subtract the powers: $\frac{x^a}{x^b} = x^{a-b}$ (e.g., $\frac{x^{10}}{x^2} = x^{10-2} = x^8$).

What is the index law for a power raised to another power (e.g., $(x^4)^3$)?

Multiply the powers: $(x^a)^b = x^{a \times b}$ (e.g., $(x^4)^3 = x^{4 \times 3} = x^{12}$).

In the straight-line equation $y = mx + c$, what do $m$ and $c$ represent?

$m$ represents the gradient (slope of the line) and $c$ represents the y-intercept (where the line crosses the y-axis).

How do you add fractions with different denominators (e.g., $\frac{1}{2} + \frac{3}{5}$)?

Make the denominators the same by multiplying top and bottom, then add the numerators: $\frac{1}{2} + \frac{3}{5} = \frac{5}{10} + \frac{6}{10} = \frac{11}{10}$.

What does the mnemonic "KFC" stand for when dividing fractions, and how is it used for $\frac{2}{7} \div \frac{3}{5}$?

Keep, Flip, Change: keep the first fraction, flip the second fraction, and change the division sign to multiplication ($\frac{2}{7} \div \frac{3}{5} = \frac{2}{7} \times \frac{5}{3} = \frac{10}{21}$).

How are the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) determined from a Venn diagram of prime factors?

The HCF is the product of the numbers in the middle (intersection), and the LCM is the product of all numbers across the entire Venn diagram.

What are the three steps to multiply decimals (e.g., $0.6 \times 0.02$)?

1. Multiply by 10s to make decimals whole numbers ($0.6 \times 10 = 6$ and $0.02 \times 100 = 2$); 2. Calculate the product ($6 \times 2 = 12$); 3. Divide by the total tens factor at the end ($12 \div 1000 = 0.012$).

What are the steps to divide decimals (e.g., $0.6 \div 0.02$)?

1. Multiply both numbers by 10s by the SAME amount to make the divisor whole ($0.6 \times 100 = 60$ and $0.02 \times 100 = 2$); 2. Calculate the division ($60 \div 2 = 30$).

What are the metric conversion values between kilograms and grams, kilometers and meters, and liters and milliliters?

$1\,\text{kg} = 1000\,\text{g}$, $1\,\text{km} = 1000\,\text{m}$, and $1\,\text{litre} = 1000\,\text{ml}$

What are the metric conversion values between meters, centimeters, and millimeters?

$1\,\text{m} = 100\,\text{cm}$ and $1\,\text{cm} = 10\,\text{mm}$