Daily Practice · Higher Plus
April 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2017 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2017A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 2nd April 2017x = 75 and y = 44, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd April 2017Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 4th April 2017y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 5th April 2017A cuboid measures 12 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th April 2017A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th April 2017On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th April 2017A car covers 400 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th April 2017f(x) = 4x + 3 and g(x) = 2x - 8. Work out fg(5).
- 10th April 2017y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 11th April 2017The 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.
- 12th April 2017A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 13th April 2017A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 14th April 2017Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 15th April 2017The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 16th April 2017y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 81.
- 17th April 2017In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 18th April 2017The probability of winning a game is 3/5. A player expects 9 wins. How many games did they play?
- 19th April 2017On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th April 2017Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 21st April 2017A quadratic sequence starts 14, 23, 34, 47. Work out the second difference, and the coefficient of n^2.
- 22nd April 2017A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd April 2017In a vector proof you find that vector PQ = 6a + 3b and vector RS = 12a + 6b. What does this show about PQ and RS?
- 24th April 2017A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 25th April 2017A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 26th April 2017A rectangle is 28 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th April 2017Solve x^2 + 8x < 0.
- 28th April 2017y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 29th April 2017A cuboid measures 10 cm by 11 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th April 2017A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?