Daily Practice · Higher Plus
April 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2016 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2016Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 2nd April 2016Simplify (x^2 - 9x + 20)/(x - 5).
- 3rd April 2016A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 4th April 2016A cuboid measures 14 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th April 2016A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th April 2016A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 7th April 2016Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 8th April 2016In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 9th April 2016y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 10th April 2016A cuboid measures 10 cm by 4 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th April 2016A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th April 2016On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th April 2016A rectangle is 18 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th April 2016Make x the subject of 7x + 2 = y(x + 2).
- 15th April 2016y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 16th April 2016The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 17th April 2016A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 18th April 2016A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 19th April 2016Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 20th April 2016Write 5/(x - 2) + 4/(x + 1) as a single fraction.
- 21st April 2016y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 49.
- 22nd April 2016In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 23rd April 2016The probability of winning a game is 1/4. A player expects 4 wins. How many games did they play?
- 24th April 2016On 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?
- 25th April 2016A block has mass 200 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th April 2016Solve 2x^2 + 3x - 20 = 0.
- 27th April 2016A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 28th April 2016In a vector proof you find that vector PQ = 6a - 2b and vector RS = 12a - 4b. What does this show about PQ and RS?
- 29th April 2016A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 30th April 2016A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?