Daily Practice · Higher Plus
April 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2022 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2022Work out the nth term of the quadratic sequence 7, 13, 21, 31, ...
- 2nd April 2022y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 3rd April 2022A cuboid measures 12 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th April 2022A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th April 2022On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th April 2022A rectangle is 26 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th April 2022The point (1, 1) lies on y = f(x). Write down its image on y = -f(x).
- 8th April 2022y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 9th April 2022A cuboid measures 12 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th April 2022A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th April 2022A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 12th April 2022Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 13th April 2022Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 14th April 2022y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 49.
- 15th April 2022The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 16th April 2022A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 17th April 2022On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th April 2022A block has mass 340 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th April 2022f(x) = 4x - 8 and g(x) = 2x + 2. Work out fg(0).
- 20th April 2022A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 21st April 2022In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 22nd April 2022The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 23rd April 2022A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 24th April 2022x = 80 and y = 50, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th April 2022The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 26th April 2022y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 27th April 2022In a vector proof you find that vector PQ = a + 2b and vector RS = 2a + 4b. What does this show about PQ and RS?
- 28th April 2022A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 29th April 2022On 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?
- 30th April 2022A car covers 720 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.