Daily Practice · Higher Plus
October 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1999A cuboid measures 12 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd October 1999A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd October 1999On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th October 1999A block has mass 600 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th October 1999Work out the coordinates of the turning point of y = x^2 + 12x + 11.
- 6th October 1999A train slows steadily from 28 m/s to rest in 8 seconds. Work out its deceleration.
- 7th October 1999A cuboid measures 7 cm by 4 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th October 1999A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th October 1999A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 10th October 1999x = 184 and y = 32, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th October 1999Simplify (x^2 - 2x - 48)/(x - 8).
- 12th October 1999y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 13th October 1999The 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.
- 14th October 1999A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 15th October 1999On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th October 1999A car covers 780 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.
- 17th October 1999In an algebraic proof, how would you write a multiple of 5 in terms of an integer n?
- 18th October 1999y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 19th October 1999In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 20th October 1999The probability of winning a game is 1/4. A player expects 30 wins. How many games did they play?
- 21st October 1999A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 22nd October 1999Rationalise the denominator of 110/sqrt(11), giving your answer in its simplest form.
- 23rd October 1999Make x the subject of 2x + 4 = y(x + 4).
- 24th October 1999y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 9.
- 25th October 1999In a vector proof you find that vector PQ = 3a + b and vector RS = 9a + 3b. What does this show about PQ and RS?
- 26th October 1999A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th October 1999On 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?
- 28th October 1999Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 29th October 1999Write 2/(x + 2) + 6/(x + 6) as a single fraction.
- 30th October 1999A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 31st October 1999A cuboid measures 15 cm by 14 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.