Daily Practice · Higher Plus
August 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1998In a vector proof you find that vector PQ = 4a - 3b and vector RS = 8a - 6b. What does this show about PQ and RS?
- 2nd August 1998A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 3rd August 1998A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 4th August 1998Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 5th August 1998A quadratic sequence starts 5, 12, 21, 32. Work out the second difference, and the coefficient of n^2.
- 6th August 1998y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 7th August 1998A cuboid measures 9 cm by 4 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th August 1998A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th August 1998On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th August 1998A block has mass 530 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th August 1998Solve x^2 - 5x - 6 > 0.
- 12th August 1998y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 13th August 1998A cuboid measures 10 cm by 11 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th August 1998A bag holds 3 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th August 1998A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 16th August 1998x = 43 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th August 1998Write x^2 + 12x - 8 in the form (x + a)^2 + b.
- 18th August 1998y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 16.
- 19th August 1998The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 20th August 1998A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 21st August 1998On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd August 1998A car covers 730 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd August 1998Work out the coordinates of the turning point of y = x^2 - 14x + 2.
- 24th August 1998A train slows steadily from 37 m/s to rest in 4 seconds. Work out its deceleration.
- 25th August 1998In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 26th August 1998The probability of winning a game is 7/8. A player expects 28 wins. How many games did they play?
- 27th August 1998A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 28th August 1998Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 29th August 1998Simplify (x^2 - 3x - 4)/(x - 4).
- 30th August 1998y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 31st August 1998In a vector proof you find that vector PQ = 6a - 4b and vector RS = 24a - 16b. What does this show about PQ and RS?