Daily Practice · Higher Plus
March 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2018A cuboid measures 5 cm by 10 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd March 2018A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd March 2018A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 4th March 2018x = 89 and y = 66, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th March 2018Write x^2 + 14x - 2 in the form (x + a)^2 + b.
- 6th March 2018y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 7th March 2018The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th March 2018A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 9th March 2018On 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?
- 10th March 2018A car covers 440 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th March 2018Work out the coordinates of the turning point of y = x^2 - 10x - 6.
- 12th March 2018y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 13th March 2018In 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.
- 14th March 2018The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 15th March 2018A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 16th March 2018Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 17th March 2018Simplify (x^2 - 4x - 5)/(x + 1).
- 18th March 2018y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 81.
- 19th March 2018In a vector proof you find that vector PQ = a + 3b and vector RS = 3a + 9b. What does this show about PQ and RS?
- 20th March 2018A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 21st March 2018On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd March 2018Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
- 23rd March 2018In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 24th March 2018A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 25th March 2018A cuboid measures 6 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th March 2018A 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?
- 27th March 2018A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 28th March 2018A rectangle is 24 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th March 2018Make x the subject of 5x + 8 = y(x + 8).
- 30th March 2018y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 31st March 2018A cuboid measures 13 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.