Daily Practice · Higher Plus
February 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2017 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2017A rectangle is 19 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd February 2017Simplify (x^2 - 7x - 8)/(x + 1).
- 3rd February 2017y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 25.
- 4th February 2017A cuboid measures 10 cm by 4 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th February 2017A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th February 2017On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th February 2017Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 8th February 2017In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 3 in terms of an integer n?
- 9th February 2017A train slows steadily from 17 m/s to rest in 10 seconds. Work out its deceleration.
- 10th February 2017The 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.
- 11th February 2017A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 12th February 2017A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 13th February 2017A block has mass 220 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th February 2017Make x the subject of 8x + 3 = y(x + 3).
- 15th February 2017y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 16th February 2017In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 17th February 2017The probability of winning a game is 5/8. A player expects 35 wins. How many games did they play?
- 18th February 2017On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th February 2017x = 86 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th February 2017Write 4/(x + 6) + 6/(x + 3) as a single fraction.
- 21st February 2017y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 22nd February 2017In a vector proof you find that vector PQ = 2a - b and vector RS = 4a - 2b. What does this show about PQ and RS?
- 23rd February 2017A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 24th February 2017A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 25th February 2017A car covers 250 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th February 2017Solve 4x^2 - 9x + 5 = 0.
- 27th February 2017y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 64.
- 28th February 2017A cuboid measures 6 cm by 9 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.