Daily Practice · Higher Plus
December 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1998A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 2nd December 1998A rectangle is 5 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd December 1998Work out the coordinates of the turning point of y = x^2 - 2x + 13.
- 4th December 1998y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 5th December 1998A cuboid measures 5 cm by 8 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th December 1998A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th December 1998On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th December 1998Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 9th December 1998Simplify (x^2 - 2x - 24)/(x + 4).
- 10th December 1998y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 11th December 1998A cuboid measures 6 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th December 1998A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th December 1998A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 14th December 1998A block has mass 620 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th December 1998In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 16th December 1998y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.
- 17th December 1998The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 18th December 1998A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 19th December 1998On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th December 1998x = 192 and y = 69, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st December 1998Make x the subject of 4x + 5 = y(x + 5).
- 22nd December 1998A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 23rd December 1998In 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.
- 24th December 1998The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 25th December 1998A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 26th December 1998A car covers 880 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.
- 27th December 1998Write 6/(x - 6) + 2/(x + 3) as a single fraction.
- 28th December 1998y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 29th December 1998In a vector proof you find that vector PQ = 3a - 5b and vector RS = 9a - 15b. What does this show about PQ and RS?
- 30th December 1998A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 31st December 1998On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?