Daily Practice · Higher Plus
January 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2001 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2001On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd January 2001Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 3rd January 2001Use the iteration x(n+1) = cube root of (12x(n) + 4) with x(0) = 1. Work out x(1) to 3 decimal places.
- 4th January 2001A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 5th January 2001The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 6th January 2001A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 7th January 2001A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 8th January 2001A block has mass 500 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.
- 9th January 2001Work out the nth term of the quadratic sequence -2, 3, 10, 19, ...
- 10th January 2001y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 11th January 2001In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 12th January 2001The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 13th January 2001On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 14th January 2001x = 129 and y = 112, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th January 2001The point (6, 5) lies on y = f(x). Write down its image on y = f(x - 1).
- 16th January 2001y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 17th January 2001In a vector proof you find that vector PQ = 5a + 5b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 18th January 2001A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 19th January 2001A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 20th January 2001A car covers 400 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st January 2001Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 22nd January 2001y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 9.
- 23rd January 2001A cuboid measures 12 cm by 14 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th January 2001A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th January 2001On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th January 2001Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 27th January 2001f(x) = 6x - 2 and g(x) = 6x + 4. Work out fg(-3).
- 28th January 2001A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 29th January 2001A cuboid measures 11 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th January 2001A bag holds 4 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st January 2001A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?