Daily Practice · Higher Plus
December 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2006On 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?
- 2nd December 2006A car covers 310 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd December 2006Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 4th December 2006A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 5th December 2006The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 6th December 2006A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 7th December 2006A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 8th December 2006Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 9th December 2006f(x) = 3x - 8 and g(x) = 4x + 7. Work out fg(-3).
- 10th December 2006y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 11th December 2006In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 12th December 2006The probability of winning a game is 2/5. A player expects 40 wins. How many games did they play?
- 13th December 2006On 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?
- 14th December 2006Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 15th December 2006The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 16th December 2006y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 17th December 2006In a vector proof you find that vector PQ = 5a + b and vector RS = 20a + 4b. What does this show about PQ and RS?
- 18th December 2006A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 19th December 2006A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 20th December 2006A rectangle is 27 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st December 2006A quadratic sequence starts 11, 29, 57, 95. Work out the second difference, and the coefficient of n^2.
- 22nd December 2006y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 4.
- 23rd December 2006A cuboid measures 14 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th December 2006A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th December 2006On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th December 2006Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 27th December 2006Solve x^2 + 3x - 4 > 0.
- 28th December 2006A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 29th December 2006A cuboid measures 8 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th December 2006A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st December 2006A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?