Daily Practice · Higher Plus
October 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1998A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 2nd October 1998A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 3rd October 1998A car covers 850 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th October 1998Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 5th October 1998y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 16.
- 6th October 1998A cuboid measures 6 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th October 1998A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th October 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?
- 9th October 1998Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 10th October 1998Use the iteration x(n+1) = cube root of (12x(n) + 5) with x(0) = 2. Work out x(1) to 3 decimal places.
- 11th October 1998A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 12th October 1998A cuboid measures 5 cm by 10 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th October 1998A bag holds 3 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th October 1998A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 15th October 1998Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 16th October 1998Work out the nth term of the quadratic sequence 10, 20, 38, 64, ...
- 17th October 1998y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 18th October 1998The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 19th October 1998A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 20th October 1998On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st October 1998A rectangle is 26 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd October 1998The point (5, 4) lies on y = f(x). Write down its image on y = f(x) - 1.
- 23rd October 1998y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 24th October 1998In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 25th October 1998The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 26th October 1998A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 27th October 1998Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
- 28th October 1998Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 29th October 1998y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 36.
- 30th October 1998In a vector proof you find that vector PQ = 3a - 3b and vector RS = 9a - 9b. What does this show about PQ and RS?
- 31st October 1998A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.