Daily Practice · Higher Plus
April 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2021 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2021A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd April 2021In a vector proof you find that vector PQ = 3a + b and vector RS = 9a + 3b. What does this show about PQ and RS?
- 3rd April 2021A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 4th April 2021A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 5th April 2021A block has mass 840 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th April 2021Work out the coordinates of the turning point of y = x^2 + 6x + 15.
- 7th April 2021y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 8th April 2021A cuboid measures 7 cm by 3 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th April 2021A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th April 2021On 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?
- 11th April 2021x = 69 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th April 2021Simplify (x^2 - 3x - 28)/(x - 7).
- 13th April 2021y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 14th April 2021A cuboid measures 4 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th April 2021A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th April 2021A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 17th April 2021A car covers 570 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th April 2021In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 19th April 2021y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 25.
- 20th April 2021The 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.
- 21st April 2021A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 22nd April 2021On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd April 2021Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 24th April 2021Make x the subject of 6x + 2 = y(x + 2).
- 25th April 2021A train slows steadily from 12 m/s to rest in 10 seconds. Work out its deceleration.
- 26th April 2021In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 27th April 2021The probability of winning a game is 9/10. A player expects 126 wins. How many games did they play?
- 28th April 2021A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 29th April 2021Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 30th April 2021Write 5/(x - 3) + 6/(x - 1) as a single fraction.