Daily Practice · Higher Plus
December 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1999A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd December 1999On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd December 1999Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 4th December 1999The point (-4, 0) lies on y = f(x). Write down its image on y = f(x) + 5.
- 5th December 1999y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 6th December 1999A cuboid measures 5 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th December 1999A bag holds 5 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th December 1999A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 9th December 1999Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
- 10th December 1999Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 11th December 1999y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 12th December 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 December 1999A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 14th December 1999On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th December 1999A rectangle is 16 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th December 1999f(x) = 4x - 7 and g(x) = 2x - 5. Work out fg(-1).
- 17th December 1999A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 18th December 1999In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 19th December 1999The probability of winning a game is 3/5. A player expects 45 wins. How many games did they play?
- 20th December 1999A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 21st December 1999Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 22nd December 1999The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 23rd December 1999y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 24th December 1999In a vector proof you find that vector PQ = 3a - 2b and vector RS = 6a - 4b. What does this show about PQ and RS?
- 25th December 1999A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 26th December 1999On 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?
- 27th December 1999A block has mass 270 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th December 1999A quadratic sequence starts 18, 33, 54, 81. Work out the second difference, and the coefficient of n^2.
- 29th December 1999y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 30th December 1999A cuboid measures 9 cm by 8 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st December 1999A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?