Daily Practice · Higher Plus
April 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2019 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2019The 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.
- 2nd April 2019A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 3rd April 2019A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 4th April 2019Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).
- 5th April 2019A quadratic sequence starts 5, 18, 39, 68. Work out the second difference, and the coefficient of n^2.
- 6th April 2019y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 7th April 2019In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 8th April 2019The probability of winning a game is 3/8. A player expects 6 wins. How many games did they play?
- 9th April 2019On 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?
- 10th April 2019A rectangle is 29 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th April 2019Solve x^2 + 9x + 14 < 0.
- 12th April 2019A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 13th April 2019In a vector proof you find that vector PQ = 2a + 4b and vector RS = 10a + 20b. What does this show about PQ and RS?
- 14th April 2019A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 15th April 2019A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 16th April 2019Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 17th April 2019Write x^2 - 16x + 15 in the form (x + a)^2 + b.
- 18th April 2019y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 19th April 2019A cuboid measures 4 cm by 14 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th April 2019A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st April 2019On 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?
- 22nd April 2019A block has mass 490 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd April 2019Work out the coordinates of the turning point of y = x^2 + 16x - 15.
- 24th April 2019y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 25th April 2019A cuboid measures 9 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th April 2019A bag holds 7 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th April 2019A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 28th April 2019x = 183 and y = 97, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th April 2019Simplify (x^2 - 5x - 14)/(x - 7).
- 30th April 2019y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.