Daily Practice · Higher Plus
September 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 1999 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1999A cuboid measures 4 cm by 8 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd September 1999A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd September 1999A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 4th September 1999A car covers 820 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.
- 5th September 1999f(x) = 4x + 4 and g(x) = 3x + 4. Work out fg(4).
- 6th September 1999y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 49.
- 7th September 1999A cuboid measures 10 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th September 1999A bag holds 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th September 1999On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th September 1999Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 11th September 1999The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 12th September 1999A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
- 13th September 1999The 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.
- 14th September 1999A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 15th September 1999A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 16th September 1999Simplify sqrt(75) + sqrt(147), giving your answer in the form a sqrt(b).
- 17th September 1999A quadratic sequence starts 10, 21, 36, 55. Work out the second difference, and the coefficient of n^2.
- 18th September 1999y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 19th September 1999In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 20th September 1999The probability of winning a game is 3/8. A player expects 30 wins. How many games did they play?
- 21st September 1999On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd September 1999A rectangle is 29 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd September 1999Solve x^2 + 2x < 0.
- 24th September 1999y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 25th September 1999In a vector proof you find that vector PQ = a - b and vector RS = 3a - 3b. What does this show about PQ and RS?
- 26th September 1999A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 27th September 1999A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 28th September 1999Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 29th September 1999Write x^2 + 6x - 8 in the form (x + a)^2 + b.
- 30th September 1999y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 36.