Daily Practice · Higher Plus
February 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2018 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2018On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 2nd February 2018Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 3rd February 2018Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 4th February 2018A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 5th February 2018The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 6th February 2018A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 7th February 2018A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 8th February 2018Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
- 9th February 2018f(x) = 6x + 4 and g(x) = 3x - 4. Work out fg(5).
- 10th February 2018y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 11th February 2018In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 12th February 2018The probability of winning a game is 3/5. A player expects 36 wins. How many games did they play?
- 13th February 2018On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th February 2018A rectangle is 21 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th February 2018The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 16th February 2018y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 17th February 2018In a vector proof you find that vector PQ = 2a - 5b and vector RS = 4a - 10b. What does this show about PQ and RS?
- 18th February 2018A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 19th February 2018A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 20th February 2018Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 21st February 2018A quadratic sequence starts 10, 27, 54, 91. Work out the second difference, and the coefficient of n^2.
- 22nd February 2018y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 49.
- 23rd February 2018A cuboid measures 4 cm by 12 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th February 2018A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th February 2018On 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?
- 26th February 2018A block has mass 650 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th February 2018Solve x^2 + 8x > 0.
- 28th February 2018A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.