Daily Practice · Higher Plus
April 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2024 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2024A block has mass 410 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd April 2024f(x) = 2x - 6 and g(x) = 5x + 3. Work out fg(4).
- 3rd April 2024y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 36.
- 4th April 2024The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 5th April 2024A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 6th April 2024On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th April 2024x = 131 and y = 37, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th April 2024The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 9th April 2024A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 10th April 2024In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 11th April 2024The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 12th April 2024A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 13th April 2024A car covers 410 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th April 2024A quadratic sequence starts 3, 17, 41, 75. Work out the second difference, and the coefficient of n^2.
- 15th April 2024y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 16th April 2024In a vector proof you find that vector PQ = 3a - b and vector RS = 6a - 2b. What does this show about PQ and RS?
- 17th April 2024A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 18th April 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?
- 19th April 2024Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 20th April 2024Solve x^2 - 6x < 0.
- 21st April 2024y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 22nd April 2024A cuboid measures 8 cm by 9 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd April 2024A bag holds 11 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th April 2024A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 25th April 2024Simplify sqrt(50) + sqrt(8), giving your answer in the form a sqrt(b).
- 26th April 2024Write x^2 + 14x + 7 in the form (x + a)^2 + b.
- 27th April 2024y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 81.
- 28th April 2024A cuboid measures 11 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th April 2024A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th April 2024On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?