Daily Practice · Higher Plus
November 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2005 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2005Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 2nd November 2005The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 3rd November 2005y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 4th November 2005A cuboid measures 12 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th November 2005A bag holds 7 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th November 2005A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 7th November 2005A block has mass 620 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th November 2005A quadratic sequence starts 11, 29, 55, 89. Work out the second difference, and the coefficient of n^2.
- 9th November 2005y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 36.
- 10th November 2005The 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.
- 11th November 2005A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 12th November 2005On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th November 2005x = 196 and y = 104, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th November 2005Solve x^2 + 5x < 0.
- 15th November 2005A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 16th November 2005In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 17th November 2005The probability of winning a game is 1/2. A player expects 6 wins. How many games did they play?
- 18th November 2005A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 19th November 2005A car covers 880 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.
- 20th November 2005Write x^2 - 12x - 11 in the form (x + a)^2 + b.
- 21st November 2005y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 22nd November 2005In a vector proof you find that vector PQ = 5a + 3b and vector RS = 15a + 9b. What does this show about PQ and RS?
- 23rd November 2005A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 24th November 2005On 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?
- 25th November 2005Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 26th November 2005Work out the coordinates of the turning point of y = x^2 - 16x + 6.
- 27th November 2005y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 28th November 2005A cuboid measures 13 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th November 2005A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th November 2005A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?