Daily Practice · Higher Plus
January 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2016A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 2nd January 2016A car covers 760 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.
- 3rd January 2016Make x the subject of 3x + 5 = y(x + 5).
- 4th January 2016y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 5th January 2016A cuboid measures 5 cm by 11 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th January 2016A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th January 2016On 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?
- 8th January 2016Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 9th January 2016Write 5/(x - 6) + 4/(x + 5) as a single fraction.
- 10th January 2016y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 11th January 2016A cuboid measures 9 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th January 2016A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th January 2016A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 14th January 2016Simplify sqrt(80) + sqrt(5), giving your answer in the form a sqrt(b).
- 15th January 2016Solve 12x^2 + 23x + 5 = 0.
- 16th January 2016y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 4.
- 17th January 2016The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 18th January 2016A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 19th January 2016On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th January 2016A rectangle is 8 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st January 2016f(x) = 6x - 12. Work out the inverse function f^-1(x).
- 22nd January 2016A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 23rd January 2016In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 24th January 2016The probability of winning a game is 1/8. A player expects 13 wins. How many games did they play?
- 25th January 2016A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 26th January 2016Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 27th January 2016Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 28th January 2016y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 29th January 2016In a vector proof you find that vector PQ = 2a - 3b and vector RS = 4a - 6b. What does this show about PQ and RS?
- 30th January 2016A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 31st January 2016On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?