Daily Practice · Higher Plus
August 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2024y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 25.
- 2nd August 2024The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 3rd August 2024A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 4th August 2024On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th August 2024A block has mass 900 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th August 2024Write x^2 + 8x - 6 in the form (x + a)^2 + b.
- 7th August 2024A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 8th August 2024In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 9th August 2024The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 10th August 2024A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 11th August 2024x = 131 and y = 42, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th August 2024Work out the coordinates of the turning point of y = x^2 + 16x + 14.
- 13th August 2024y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 14th August 2024In a vector proof you find that vector PQ = 5a + 3b and vector RS = 10a + 6b. What does this show about PQ and RS?
- 15th August 2024A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 16th August 2024On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th August 2024A car covers 820 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th August 2024Simplify (x^2 - 11x + 28)/(x - 4).
- 19th August 2024y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 20th August 2024A cuboid measures 14 cm by 15 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st August 2024A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd August 2024A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 23rd August 2024Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.
- 24th August 2024In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 25th August 2024y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 9.
- 26th August 2024A cuboid measures 8 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th August 2024A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th August 2024On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th August 2024Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
- 30th August 2024Make x the subject of 8x + 3 = y(x + 3).
- 31st August 2024A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.