Daily Practice · Higher Plus
January 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2000 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2000A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 2nd January 2000x = 117 and y = 58, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd January 2000Solve x^2 + 7x + 12 < 0.
- 4th January 2000y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 49.
- 5th January 2000A cuboid measures 6 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th January 2000A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th January 2000On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th January 2000A car covers 520 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th January 2000Write x^2 + 8x + 1 in the form (x + a)^2 + b.
- 10th January 2000A train slows steadily from 37 m/s to rest in 8 seconds. Work out its deceleration.
- 11th January 2000The 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.
- 12th January 2000A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 13th January 2000A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 14th January 2000Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 15th January 2000Work out the coordinates of the turning point of y = x^2 + 12x - 10.
- 16th January 2000y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 17th January 2000In 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.
- 18th January 2000The probability of winning a game is 1/8. A player expects 12 wins. How many games did they play?
- 19th January 2000On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th January 2000Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 21st January 2000Simplify (x^2 - 9x + 8)/(x - 8).
- 22nd January 2000y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 23rd January 2000In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 24th January 2000A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 25th January 2000A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 26th January 2000A rectangle is 13 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th January 2000In an algebraic proof, how would you write an even number in terms of an integer n?
- 28th January 2000y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 16.
- 29th January 2000A cuboid measures 8 cm by 12 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th January 2000A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st January 2000On 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?