Question 1

A TRIANGLE HAS A BASE OF 12 CM, A PERPENDICULAR HEIGHT OF 5 CM AND A SLANTED SIDE OF 13 CM. WHAT IS ITS AREA?

Accepted Answer

30 CM². Use the perpendicular height, not the slanted side: ½ × 12 × 5 = 30 cm². Using the 13 cm side gives 78 cm², and leaving out the half gives 60 cm².

Question 2

A PARALLELOGRAM HAS BASE 8 CM AND PERPENDICULAR HEIGHT 5 CM. ITS AREA IN CM² IS ___.

Accepted Answer

FORTY. A parallelogram has no half in its formula, so the area is 8 × 5 = 40 cm². Halving it would give the area of a triangle with the same base and height.

Question 3

A CYLINDRICAL TIN HAS A RADIUS OF 4 CM AND A HEIGHT OF 10 CM. WHAT IS ITS VOLUME IN TERMS OF π?

Accepted Answer

160π CM³. The circular end has area π × 4² = 16π, and multiplying by the height 10 gives 160π cm³. Forgetting to square the radius gives 40π, and using the diameter instead gives 400π.

Question 4

A CYCLIST TRAVELS 45 KM IN 90 MINUTES. WHAT IS HER AVERAGE SPEED IN KM/H?

Accepted Answer

30 KM/H. Convert 90 minutes to 1.5 hours first, then 45 ÷ 1.5 = 30 km/h. Dividing 45 by 90 gives 0.5, but that is kilometres per minute, not per hour.

Question 5

X⁹ ÷ X⁴ SIMPLIFIES TO X TO THE POWER ___.

Accepted Answer

FIVE. When dividing powers of the same base you subtract the indices: 9 − 4 = 5, so the answer is x⁵. Adding them would give x¹³, which is the rule for multiplying.

Question 6

A METAL BLOCK HAS A MASS OF 540 G AND A VOLUME OF 200 CM³. WHAT IS ITS DENSITY?

Accepted Answer

2.7 G/CM³. Divide mass by volume: 540 ÷ 200 = 2.7 g/cm³. Dividing the other way round gives 0.37, which would be the volume per gram rather than the density.

Question 7

A GAME COSTS £25 IN A SALE, REDUCED FROM £40. WHAT IS THE PERCENTAGE REDUCTION?

Accepted Answer

37.5%. The reduction is £15, and it is measured against the original price: 15 ÷ 40 × 100 = 37.5%. Dividing by £25 gives 60%, which is the common slip.

Question 8

A COAT IS REDUCED BY 20% TO £48 IN A SALE. WHAT WAS THE ORIGINAL PRICE?

Accepted Answer

£60. The sale price is 80% of the original, so the multiplier is 0.8 and the original is 48 ÷ 0.8 = £60. Adding 20% to £48 gives £57.60, which is not the price before the sale.

Question 9

EACH INTERIOR ANGLE OF A REGULAR POLYGON IS 150°. THE POLYGON HAS ___ SIDES.

Accepted Answer

TWELVE. Work from the angle on the outside: 180 − 150 = 30° for each corner. A full turn is 360°, so 360 ÷ 30 gives 12 sides. Check: ten sides would leave interior angles of 144°.

Question 10

A STRAIGHT LINE PASSES THROUGH (0, 4) AND (3, 13). ITS GRADIENT IS ___.

Accepted Answer

THREE. The line rises 13 − 4 = 9 while moving 3 across, so the gradient is 9 ÷ 3 = 3. The y-intercept is 4, giving the equation y = 3x + 4.

Question 11

A STRAIGHT LINE PASSES THROUGH (2, 7) AND (6, 19). WHAT IS ITS EQUATION?

Accepted Answer

Y = 3X + 1. The gradient is (19 − 7) ÷ (6 − 2) = 3. Substituting (2, 7) into y = 3x + c gives 7 = 6 + c, so c = 1. The option y = 4x − 1 passes through (2, 7) but misses (6, 19).

Question 12

WHAT IS THE NTH TERM OF THE SEQUENCE 7, 11, 15, 19, ...?

Accepted Answer

4N + 3. The terms go up by 4, so the nth term starts 4n. Term 1 would be 4, but it is 7, so add 3: 4n + 3. Check with n = 4: 16 + 3 = 19.

Question 13

THE MEDIAN OF 15 VALUES IN ORDER IS THE VALUE IN POSITION NUMBER ___.

Accepted Answer

EIGHT. The median sits in position (15 + 1) ÷ 2 = 8, with seven values below it and seven above. For 14 values the position would be 7.5, midway between the 7th and 8th.

Question 14

5 CHILDREN HAVE 0 PETS, 8 HAVE 1 PET, 4 HAVE 2 PETS AND 3 HAVE 3 PETS. WHAT IS THE MEAN NUMBER OF PETS?

Accepted Answer

1.25. Multiply each value by its frequency: 0 + 8 + 8 + 9 = 25 pets. There are 5 + 8 + 4 + 3 = 20 children, so the mean is 25 ÷ 20 = 1.25. Averaging 0, 1, 2 and 3 gives 1.5, which ignores the frequencies.

Question 15

A BAG HOLDS 3 RED AND 7 BLUE COUNTERS. A COUNTER IS PICKED AND REPLACED 50 TIMES. THE EXPECTED NUMBER OF RED COUNTERS IS ___.

Accepted Answer

FIFTEEN. The probability of red is 3/10, so the expected number in 50 picks is 3/10 × 50 = 15. The real count will usually differ a little because this is only a prediction.

Question 16

TWO INDEPENDENT EVENTS HAVE PROBABILITIES 0.4 AND 0.5. WHAT IS THE PROBABILITY THAT BOTH HAPPEN?

Accepted Answer

0.2. For independent events you multiply: 0.4 × 0.5 = 0.2. Adding gives 0.9, which would be nonsense here because it is bigger than either chance on its own.

Formulas to Memorise