Daily Practice · Higher Plus
November 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2010 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2010y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 2nd November 2010A cuboid measures 15 cm by 12 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd November 2010A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th November 2010A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 5th November 2010Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 6th November 2010f(x) = 5x - 6 and g(x) = 2x - 9. Work out fg(6).
- 7th November 2010y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 16.
- 8th November 2010A cuboid measures 14 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th November 2010A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th November 2010On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th November 2010Simplify sqrt(50) + sqrt(50), giving your answer in the form a sqrt(b).
- 12th November 2010The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 13th November 2010A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 14th November 2010The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 15th November 2010A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 16th November 2010A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 17th November 2010A rectangle is 13 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th November 2010A quadratic sequence starts 7, 28, 59, 100. Work out the second difference, and the coefficient of n^2.
- 19th November 2010y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 20th November 2010In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 21st November 2010The probability of winning a game is 1/5. A player expects 11 wins. How many games did they play?
- 22nd November 2010On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd November 2010Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 24th November 2010Solve x^2 - 3x - 4 < 0.
- 25th November 2010y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 26th November 2010In a vector proof you find that vector PQ = 6a - b and vector RS = 18a - 3b. What does this show about PQ and RS?
- 27th November 2010A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 28th November 2010A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 29th November 2010A block has mass 890 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th November 2010Write x^2 + 8x - 1 in the form (x + a)^2 + b.