Daily Practice · Higher Plus
December 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1996A quadratic sequence starts 8, 13, 24, 41. Work out the second difference, and the coefficient of n^2.
- 2nd December 1996y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 64.
- 3rd December 1996In 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.
- 4th December 1996The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 5th December 1996On 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?
- 6th December 1996Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 7th December 1996Solve x^2 + 12x + 35 > 0.
- 8th December 1996A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 9th December 1996In a vector proof you find that vector PQ = 4a - 2b and vector RS = 20a - 10b. What does this show about PQ and RS?
- 10th December 1996A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 11th December 1996A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 12th December 1996Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
- 13th December 1996Write x^2 - 4x + 7 in the form (x + a)^2 + b.
- 14th December 1996y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 15th December 1996A cuboid measures 5 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th December 1996A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th December 1996On 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?
- 18th December 1996A rectangle is 18 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th December 1996Work out the coordinates of the turning point of y = x^2 + 12x - 14.
- 20th December 1996y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 21st December 1996A cuboid measures 6 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd December 1996A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd December 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 24th December 1996Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
- 25th December 1996Simplify (x^2 - 15x + 56)/(x - 8).
- 26th December 1996y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 36.
- 27th December 1996The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 28th December 1996A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 29th December 1996On 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?
- 30th December 1996A block has mass 200 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st December 1996In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?