Daily Practice · Higher Plus
November 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 1998 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1998On 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?
- 2nd November 1998A block has mass 820 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd November 1998f(x) = 4x + 5 and g(x) = 3x + 8. Work out fg(6).
- 4th November 1998A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 5th November 1998A cuboid measures 4 cm by 13 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th November 1998A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th November 1998A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 8th November 1998x = 40 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th November 1998The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 10th November 1998y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 11th November 1998A cuboid measures 13 cm by 11 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th November 1998A bag holds 7 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th November 1998On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th November 1998A car covers 460 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th November 1998A quadratic sequence starts 2, 1, 2, 5. Work out the second difference, and the coefficient of n^2.
- 16th November 1998y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 17th November 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 November 1998A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 19th November 1998A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 20th November 1998Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.
- 21st November 1998Solve x^2 + 13x + 40 < 0.
- 22nd November 1998y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
- 23rd November 1998In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 24th November 1998The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 25th November 1998On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 26th November 1998Simplify sqrt(45) + sqrt(180), giving your answer in the form a sqrt(b).
- 27th November 1998Write x^2 + 2x + 13 in the form (x + a)^2 + b.
- 28th November 1998A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 29th November 1998In a vector proof you find that vector PQ = a - 6b and vector RS = 5a - 30b. What does this show about PQ and RS?
- 30th November 1998A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.