Daily Practice · Higher Plus
January 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2020A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 2nd January 2020In 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.
- 3rd January 2020The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 4th January 2020A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 5th January 2020x = 162 and y = 152, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th January 2020Work out the nth term of the quadratic sequence -6, -1, 10, 27, ...
- 7th January 2020y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 8th January 2020In a vector proof you find that vector PQ = 2a + 5b and vector RS = 6a + 15b. What does this show about PQ and RS?
- 9th January 2020A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 10th January 2020On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th January 2020A car covers 770 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th January 2020The point (5, -6) lies on y = f(x). Write down its image on y = f(x) - 6.
- 13th January 2020y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 14th January 2020A cuboid measures 3 cm by 10 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th January 2020A bag holds 11 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th January 2020A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 17th January 2020Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.
- 18th January 2020Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 19th January 2020y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 25.
- 20th January 2020A cuboid measures 10 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st January 2020A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd January 2020On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd January 2020Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 24th January 2020f(x) = 2x + 2 and g(x) = 2x - 4. Work out fg(4).
- 25th January 2020A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 26th January 2020The 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.
- 27th January 2020A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 28th January 2020A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 29th January 2020A rectangle is 16 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th January 2020The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 31st January 2020y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.