GCSE Mathematics Higher Tier Practice Assessment 1

Vocabulary practice flashcards based on the GCSE Mathematics Higher Tier Mini practice assessment and mark scheme.

Standard Form of $0.000583$

The representation of $0.000583$ in standard form, which is $5.83 \times 10^{-4}$.

Fully Simplified Form of $\sqrt{50} - 2\sqrt{8}$

The surd expression evaluated to its simplest single-surd form, equal to $\sqrt{2}$ (derived from $\sqrt{50} = 5\sqrt{2}$ and $2\sqrt{8} = 4\sqrt{2}$).

Expansion of $(2x - 3)(x + 4)$

The expanded and simplified algebraic expression equal to $2x^2 + 5x - 12$.

Solutions to $x^2 - 5x + 6 = 0$

The values of $x$ satisfying the quadratic equation, which are $x = 2$ or $x = 3$.

Volume of Water in Ratio $2 : 7$

The volume of water used when making $1.35\,\text{litres}$ of drink with squash and water in a $2 : 7$ ratio, equal to $7 \times 0.15 = 1.05\,\text{litres}$.

Original Price (Reverse Percentage)

The starting price before a $15\%$ reduction when the sale price is $£51$, calculated as $£51 \div 0.85 = £60$.

Hypotenuse of Shorter Sides $7\,\text{cm}$ and $9\,\text{cm}$

The length of the hypotenuse in a right-angled triangle calculated via Pythagoras' theorem as $\sqrt{7^2 + 9^2} = \sqrt{130} \approx 11.4\,\text{cm}$ (to 3 significant figures).

Probability of Two Red Counters Without Replacement

The probability of randomly drawing two red counters consecutively from a bag containing 5 red and 3 blue counters, calculated as $\frac{5}{8} \times \frac{4}{7} = \frac{5}{14}$.

Next Term of Sequence $5, 12, 21, 32, \dots$

The fifth term in the quadratic sequence $5, 12, 21, 32, \dots$, which is $45$.

$n^{\text{th}}$ Term of Sequence $5, 12, 21, 32, \dots$

The general algebraic formula defining the sequence $5, 12, 21, 32, \dots$, given by the expression $n^2 + 4n$.

Average Speed ($156\,\text{km}$ in $2\,\text{hours } 24\,\text{minutes}$)

The average rate of travel calculated as total distance divided by total time in decimal hours ($156 \div 2.4$), yielding $65\,\text{km/h}$.

Percentage Increase in Area from $20\%$ Dimension Increase

The actual percentage increase in the area of a rectangle when both dimensions are increased by $20\%$, which is $44\%$ (demonstrated by a $10 \times 10 = 100$ rectangle increasing to $12 \times 12 = 144$).