Daily Practice · Higher Plus
April 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2020 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2020In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 2nd April 2020The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 3rd April 2020On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th April 2020A car covers 550 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th April 2020Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 6th April 2020A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 7th April 2020In a vector proof you find that vector PQ = 6a - 5b and vector RS = 24a - 20b. What does this show about PQ and RS?
- 8th April 2020A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 9th April 2020A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 10th April 2020Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 11th April 2020Use the iteration x(n+1) = cube root of (9x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 12th April 2020y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 13th April 2020A cuboid measures 5 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th April 2020A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th April 2020On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th April 2020Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
- 17th April 2020Work out the nth term of the quadratic sequence 2, 12, 28, 50, ...
- 18th April 2020y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 19th April 2020A cuboid measures 6 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th April 2020A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st April 2020A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 22nd April 2020A rectangle is 20 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd April 2020The point (-4, -6) lies on y = f(x). Write down its image on y = -f(x).
- 24th April 2020y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
- 25th April 2020The 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.
- 26th April 2020A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 27th April 2020On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th April 2020Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 29th April 2020Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 30th April 2020A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.