Daily Practice · Higher Plus
November 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 1999 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 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?
- 2nd November 1999A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 3rd November 1999A rectangle is 28 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th November 1999Solve 15x^2 + 14x - 8 = 0.
- 5th November 1999y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 6th November 1999A cuboid measures 12 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th November 1999A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th November 1999On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th November 1999Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 10th November 1999f(x) = 8x - 2. Work out the inverse function f^-1(x).
- 11th November 1999y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 12th November 1999The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 13th November 1999A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 14th November 1999A 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 November 1999A block has mass 230 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th November 1999Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 17th November 1999y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 81.
- 18th November 1999In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 19th November 1999The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?
- 20th November 1999On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st November 1999x = 77 and y = 37, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd November 1999Use the iteration x(n+1) = cube root of (4x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 23rd November 1999A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 24th November 1999In a vector proof you find that vector PQ = 6a + 2b and vector RS = 18a + 6b. What does this show about PQ and RS?
- 25th November 1999A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 26th November 1999A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 27th November 1999A car covers 350 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th November 1999Work out the nth term of the quadratic sequence -5, 0, 11, 28, ...
- 29th November 1999y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 30th November 1999A cuboid measures 10 cm by 3 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.