Daily Practice · Higher Plus
March 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2017A 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?
- 2nd March 2017On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd March 2017Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 4th March 2017f(x) = 3x + 3. Work out the inverse function f^-1(x).
- 5th March 2017A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 6th March 2017A cuboid measures 13 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th March 2017A bag holds 3 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th March 2017A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 9th March 2017Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 10th March 2017Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 11th March 2017y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 12th March 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.
- 13th March 2017A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 14th March 2017On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th March 2017A rectangle is 18 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th March 2017Use the iteration x(n+1) = cube root of (3x(n) + 9) with x(0) = 1. Work out x(1) to 3 decimal places.
- 17th March 2017y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 18th March 2017In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 19th March 2017The probability of winning a game is 3/8. A player expects 6 wins. How many games did they play?
- 20th March 2017A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 21st March 2017Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 22nd March 2017Work out the nth term of the quadratic sequence 6, 20, 42, 72, ...
- 23rd March 2017y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 16.
- 24th March 2017In a vector proof you find that vector PQ = 6a - b and vector RS = 18a - 3b. What does this show about PQ and RS?
- 25th March 2017A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 26th March 2017On 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?
- 27th March 2017A block has mass 380 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th March 2017The point (-1, 1) lies on y = f(x). Write down its image on y = f(x - 5).
- 29th March 2017A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 30th March 2017A cuboid measures 11 cm by 5 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st March 2017A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?