Daily Practice · Higher Plus
December 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2003Solve x^2 + 9x + 14 > 0.
- 2nd December 2003y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 3rd December 2003In a vector proof you find that vector PQ = 2a + b and vector RS = 10a + 5b. What does this show about PQ and RS?
- 4th December 2003A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th December 2003On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th December 2003A car covers 830 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th December 2003Write x^2 - 10x - 3 in the form (x + a)^2 + b.
- 8th December 2003y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 9th December 2003A cuboid measures 15 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th December 2003A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th December 2003A 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?
- 12th December 2003Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 13th December 2003Work out the coordinates of the turning point of y = x^2 + 14x - 3.
- 14th December 2003y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 25.
- 15th December 2003A cuboid measures 10 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th December 2003A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th December 2003On 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?
- 18th December 2003Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
- 19th December 2003Simplify (x^2 - 15x + 56)/(x - 7).
- 20th December 2003A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 21st December 2003The 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.
- 22nd December 2003A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 23rd December 2003A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 24th December 2003A rectangle is 6 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th December 2003In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 26th December 2003y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 27th December 2003In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 28th December 2003The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 29th December 2003On 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?
- 30th December 2003Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 31st December 2003Make x the subject of 7x + 6 = y(x + 6).