Daily Practice · Higher Plus
April 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2023 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2023A car covers 400 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd April 2023In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 3rd April 2023y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 4th April 2023A cuboid measures 11 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th April 2023A bag holds 3 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th April 2023A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 7th April 2023Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 8th April 2023Make x the subject of 8x + 6 = y(x + 6).
- 9th April 2023y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 81.
- 10th April 2023The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 11th April 2023A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 12th April 2023On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th April 2023Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
- 14th April 2023Write 2/(x - 1) + 5/(x + 5) as a single fraction.
- 15th April 2023A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 16th April 2023In 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.
- 17th April 2023The probability of winning a game is 7/8. A player expects 35 wins. How many games did they play?
- 18th April 2023A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 19th April 2023A rectangle is 4 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th April 2023Solve 4x^2 + 21x + 5 = 0.
- 21st April 2023y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 22nd April 2023In a vector proof you find that vector PQ = a + 5b and vector RS = 2a + 10b. What does this show about PQ and RS?
- 23rd April 2023A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 24th April 2023On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th April 2023Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 26th April 2023f(x) = 7x + 7. Work out the inverse function f^-1(x).
- 27th April 2023y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 28th April 2023A cuboid measures 11 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th April 2023A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th April 2023A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?