Daily Practice · Higher Plus
April 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2018 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2018A bag holds 5 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd April 2018On 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?
- 3rd April 2018Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
- 4th April 2018Write 5/(x - 1) + 5/(x - 3) as a single fraction.
- 5th April 2018y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 6th April 2018The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 7th April 2018A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 8th April 2018A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 9th April 2018A block has mass 260 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.
- 10th April 2018Solve 12x^2 - 11x - 15 = 0.
- 11th April 2018y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 25.
- 12th April 2018In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 13th April 2018The probability of winning a game is 9/10. A player expects 99 wins. How many games did they play?
- 14th April 2018On 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?
- 15th April 2018x = 188 and y = 151, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th April 2018f(x) = 4x + 6. Work out the inverse function f^-1(x).
- 17th April 2018A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 18th April 2018In a vector proof you find that vector PQ = a - b and vector RS = 2a - 2b. What does this show about PQ and RS?
- 19th April 2018A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 20th April 2018A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 21st April 2018A car covers 680 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd April 2018Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 23rd April 2018y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 24th April 2018A cuboid measures 5 cm by 11 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th April 2018A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th April 2018On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th April 2018Rationalise the denominator of 21/sqrt(7), giving your answer in its simplest form.
- 28th April 2018Use the iteration x(n+1) = cube root of (9x(n) + 5) with x(0) = 1. Work out x(1) to 3 decimal places.
- 29th April 2018y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 30th April 2018A cuboid measures 7 cm by 10 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.