Daily Practice · Higher Plus
July 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2019A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 2nd July 2019On 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?
- 3rd July 2019A rectangle is 4 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th July 2019f(x) = 2x - 7 and g(x) = 5x + 5. Work out fg(-2).
- 5th July 2019y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 6th July 2019In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 7th July 2019The probability of winning a game is 3/8. A player expects 9 wins. How many games did they play?
- 8th July 2019A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 9th July 2019Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 10th July 2019The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 11th July 2019y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 49.
- 12th July 2019In a vector proof you find that vector PQ = 6a + 6b and vector RS = 18a + 18b. What does this show about PQ and RS?
- 13th July 2019A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 14th July 2019On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th July 2019A block has mass 440 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th July 2019A quadratic sequence starts 8, 21, 42, 71. Work out the second difference, and the coefficient of n^2.
- 17th July 2019A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 18th July 2019A cuboid measures 5 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th July 2019A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th July 2019A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 21st July 2019x = 189 and y = 155, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd July 2019Solve x^2 + x - 12 < 0.
- 23rd July 2019y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 24th July 2019A cuboid measures 9 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th July 2019A 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?
- 26th July 2019On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th July 2019A car covers 180 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.
- 28th July 2019Write x^2 - 16x + 3 in the form (x + a)^2 + b.
- 29th July 2019y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 30th July 2019The 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.
- 31st July 2019A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.