Daily Practice · Higher Plus
January 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2019The 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.
- 2nd January 2019A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 3rd January 2019On 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?
- 4th January 2019Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 5th January 2019Write x^2 - 8x + 1 in the form (x + a)^2 + b.
- 6th January 2019A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 7th January 2019In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 8th January 2019The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 9th January 2019A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 10th January 2019Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
- 11th January 2019Work out the coordinates of the turning point of y = x^2 - 8x - 7.
- 12th January 2019y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 13th January 2019In a vector proof you find that vector PQ = 5a - 5b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 14th January 2019A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 15th January 2019On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th January 2019A rectangle is 7 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th January 2019Simplify (x^2 + x - 6)/(x + 3).
- 18th January 2019y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 19th January 2019A cuboid measures 14 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th January 2019A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st January 2019A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 22nd January 2019Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 23rd January 2019In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 24th January 2019y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 4.
- 25th January 2019A cuboid measures 14 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th January 2019A bag holds 5 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th January 2019On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th January 2019A block has mass 360 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th January 2019Make x the subject of 2x + 2 = y(x + 2).
- 30th January 2019A train slows steadily from 12 m/s to rest in 8 seconds. Work out its deceleration.
- 31st January 2019The 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.