Drill Pack 1 (easy mix) - Year selective Mathematics

Format

$20$ questions.
Mixed topics (number, fractions, percents, ratios, algebra, geometry, probability).
Each question has a single numeric or short-form answer.
Write answers on a separate sheet numbered 1-20.

Drill timer

Count down

00:00

Target: 25:00

Previous attempts

No attempts yet.

Target: 25 minutes. Time yourself with a watch or phone timer — no pausing.

Questions

Fluency

Drill Pack 1 — 25 minutes

Evaluate $-7 + 12 - 5$ .
$\dfrac{3}{4} + \dfrac{1}{2}$ as a single fraction.
$25\%$ of $160$ .
Simplify the ratio $18 : 24$ .
Solve $3x + 4 = 19$ .
Round $3.748$ to $1$ decimal place.
A rectangle is $7$ cm by $4$ cm. Perimeter?
Area of a triangle with base $6$ cm and height $5$ cm?
$0.6$ written as a fraction in simplest form.
Next term of $2, 5, 8, 11, \ldots$
The mean of $4, 6, 8, 10, 12$ .
$P(\text{even})$ when rolling a fair six-sided die.
Expand $4(x - 3)$ .
If $x = 5$ , evaluate $2x^2 - 3$ .
A car travels $180$ km in $3$ hours. Average speed in km/h?
Write $\dfrac{3}{5}$ as a percentage.
A triangle has angles $50^\circ$ , $60^\circ$ , and $x$ . Find $x$ .
Simplify $8a - 3a + 2a$ .
$12^2$ .
Which is larger: $\dfrac{2}{3}$ or $0.65$ ?

Answers

Answer key

Attempt the practice first. When you're ready to check, expand the answers below.

Show the full answer key

Each answer includes a strategy note: the quickest method, and a trap to avoid. The fastest method is rarely “do all the arithmetic”.

$0$ . Quick: group signs, $(-7 - 5) + 12 = -12 + 12 = 0$ . Trap: don’t compute left-to-right if a cancellation is obvious.
$\dfrac{5}{4}$ (or $1\tfrac{1}{4}$ ). Quick: common denominator $4$ : $\tfrac{3}{4} + \tfrac{2}{4}$ . Trap: don’t add denominators.
$40$ . Quick: $25\%$ is $\tfrac{1}{4}$ , so divide by $4$ . Trap: $25\%$ of $160$ is not $25 \times 1.6 = 40$ by coincidence — always convert the percent to a fraction first.
$3 : 4$ . Quick: HCF of $18$ and $24$ is $6$ , divide both by $6$ .
$x = 5$ . Quick: $3x = 15$ , $x = 5$ . Trap: do “undo + 4” before “undo $\times 3$ ”.
$3.7$ . Quick: the digit after the $7$ is a $4$ , so round down.
$22$ cm. Quick: $2(7 + 4) = 22$ .
$15$ cm $^2$ . Quick: $\tfrac{1}{2} \times 6 \times 5$ . Trap: don’t forget the $\tfrac{1}{2}$ .
$\dfrac{3}{5}$ . Quick: $0.6 = \tfrac{6}{10} = \tfrac{3}{5}$ .
$14$ . Quick: common difference is $+3$ .
$8$ . Quick: the middle number of a symmetric arithmetic set equals the mean.
$\dfrac{1}{2}$ . Quick: $2, 4, 6$ out of $6$ . Trap: don’t rewrite as $\tfrac{3}{6}$ if you can spot $\tfrac{1}{2}$ immediately.
$4x - 12$ . Quick: distributive law.
$47$ . Quick: $2(25) - 3 = 50 - 3 = 47$ . Trap: " $2x^2$ " means $2 \cdot x^2$ , not $(2x)^2$ .
$60$ km/h. Quick: $180 \div 3 = 60$ .
$60\%$ . Quick: $\tfrac{3}{5} = \tfrac{60}{100}$ .
$70^\circ$ . Quick: $180 - 50 - 60 = 70$ .
$7a$ . Quick: $8 - 3 + 2 = 7$ .
$144$ . Memorise squares up to $15^2 = 225$ — comes up constantly.
$0.65$ . Quick: $\tfrac{2}{3} \approx 0.667$ , just above $0.65$ . So $\tfrac{2}{3}$ is larger. Trap: reread “which is larger” — test-writers put the tempting wrong answer first.

Self-check

Score out of 20: _______ / 20
Time taken: _______ minutes
Questions skipped or guessed: _______
Questions I’d redo without help: _______

Prefer paper? Print the answer key as a separate booklet: open print view ->