Daily Practice · Higher Plus
January 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2018A bag holds 5 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd January 2018A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 3rd January 2018A rectangle is 4 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th January 2018f(x) = 5x - 8. Work out the inverse function f^-1(x).
- 5th January 2018y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 36.
- 6th January 2018The 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.
- 7th January 2018A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 8th January 2018On 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?
- 9th January 2018Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 10th January 2018Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 11th January 2018A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 12th January 2018In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 13th January 2018The probability of winning a game is 4/5. A player expects 12 wins. How many games did they play?
- 14th January 2018A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 15th January 2018A block has mass 520 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th January 2018Use the iteration x(n+1) = cube root of (4x(n) + 5) with x(0) = 3. Work out x(1) to 3 decimal places.
- 17th January 2018y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 18th January 2018In a vector proof you find that vector PQ = 2a - b and vector RS = 8a - 4b. What does this show about PQ and RS?
- 19th January 2018A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th January 2018On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st January 2018x = 67 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd January 2018Work out the nth term of the quadratic sequence 3, 13, 31, 57, ...
- 23rd January 2018y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 24th January 2018A cuboid measures 5 cm by 8 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th January 2018A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th January 2018A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 27th January 2018A car covers 270 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th January 2018The point (-1, -6) lies on y = f(x). Write down its image on y = f(x - 3).
- 29th January 2018y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 36.
- 30th January 2018A cuboid measures 7 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st January 2018A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?